<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Factoring Trinomials</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 10px 12px;
      gap: 10px;
      max-width: 620px;
      margin: 0 auto;
    }

    /* Header Equation Bar */
    .equation-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 6px;
      font-size: 17px;
      font-weight: 700;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 14px;
      width: 100%;
      text-align: center;
    }

    .eq-part {
      display: inline-flex;
      align-items: center;
    }

    .term-b { color: #0284c7; }
    .term-c { color: #d97706; }
    .term-p { color: #059669; }
    .term-q { color: #7c3aed; }

    /* Dual Models Container */
    .models-container {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
    }

    @media (max-width: 500px) {
      .models-container {
        grid-template-columns: 1fr;
        gap: 10px;
      }
    }

    .model-card {
      display: flex;
      flex-direction: column;
      align-items: center;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 6px;
      position: relative;
    }

    .model-title {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.6px;
      color: #64748b;
      margin-bottom: 4px;
    }

    /* Diamond / X-Factor Model */
    .diamond-wrap {
      width: 180px;
      height: 180px;
      position: relative;
    }

    .diamond-svg {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
    }

    .diamond-cell {
      position: absolute;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      text-align: center;
      border-radius: 6px;
      padding: 2px 4px;
      cursor: pointer;
      user-select: none;
      transition: background 0.15s ease, box-shadow 0.15s ease;
    }

    .cell-top {
      top: 4px;
      left: 50%;
      transform: translateX(-50%);
      width: 120px;
      height: 48px;
    }

    .cell-bottom {
      bottom: 4px;
      left: 50%;
      transform: translateX(-50%);
      width: 120px;
      height: 48px;
    }

    .cell-left {
      left: 2px;
      top: 50%;
      transform: translateY(-50%);
      width: 48px;
      height: 52px;
    }

    .cell-right {
      right: 2px;
      top: 50%;
      transform: translateY(-50%);
      width: 48px;
      height: 52px;
    }

    .tag-label {
      font-size: 9px;
      font-weight: 700;
      text-transform: uppercase;
      line-height: 1.1;
    }

    .tag-top { color: #b45309; }
    .tag-bottom { color: #0284c7; }
    .tag-left { color: #047857; }
    .tag-right { color: #6d28d9; }

    .val-math {
      font-size: 13px;
      font-weight: 700;
      line-height: 1.2;
    }

    .val-sub {
      font-size: 10px;
      font-weight: 600;
      color: #64748b;
    }

    /* Area Model 2x2 */
    .area-grid {
      display: grid;
      grid-template-columns: 28px 74px 74px;
      grid-template-rows: 24px 72px 72px;
      gap: 4px;
      align-items: center;
      justify-items: center;
      margin-top: 2px;
    }

    .area-header {
      font-size: 13px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
      width: 100%;
      height: 100%;
      border-radius: 4px;
    }

    .hdr-x { color: #334155; }
    .hdr-p { color: #047857; background: #ecfdf5; }
    .hdr-q { color: #6d28d9; background: #f5f3ff; }

    .area-box {
      width: 100%;
      height: 100%;
      border-radius: 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      border: 1.5px solid transparent;
      cursor: pointer;
      font-size: 14px;
      font-weight: 700;
      text-align: center;
      padding: 2px;
      transition: background 0.15s ease, box-shadow 0.15s ease;
    }

    .box-sub {
      font-size: 10px;
      font-weight: 600;
      opacity: 0.85;
      margin-top: 2px;
    }

    .box-x2 {
      background: #f1f5f9;
      border-color: #cbd5e1;
      color: #1e293b;
    }

    .box-qx {
      background: #f5f3ff;
      border-color: #ddd6fe;
      color: #6d28d9;
    }

    .box-px {
      background: #ecfdf5;
      border-color: #a7f3d0;
      color: #047857;
    }

    .box-pq {
      background: #fffbeb;
      border-color: #fde68a;
      color: #b45309;
    }

    /* Link Hover / Focus Highlight */
    .highlight-active {
      box-shadow: 0 0 0 2px #2563eb !important;
      background-color: #eff6ff !important;
    }

    /* Interactive Preset Switcher */
    .controls {
      display: flex;
      gap: 8px;
      width: 100%;
      justify-content: center;
    }

    .btn-preset {
      flex: 1;
      max-width: 175px;
      padding: 7px 6px;
      font-size: 12px;
      font-weight: 700;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      background: #f8fafc;
      color: #334155;
      cursor: pointer;
      text-align: center;
      transition: all 0.15s ease;
      white-space: nowrap;
    }

    .btn-preset:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }

    .btn-preset.active {
      background: #eff6ff;
      border-color: #3b82f6;
      color: #1d4ed8;
      box-shadow: 0 1px 3px rgba(37, 99, 235, 0.15);
    }
  </style>
</head>
<body>

  
  <div class="equation-bar" id="eqBar"></div>

  
  <div class="models-container">
    
    
    <div class="model-card">
      <div class="model-title">Diamond / X-Factor Model</div>
      <div class="diamond-wrap">
        <svg class="diamond-svg" viewBox="0 0 180 180" aria-hidden="true">
          
          <polygon points="90,6 174,90 90,174 6,90" fill="none" stroke="#e2e8f0" stroke-width="1.5" stroke-dasharray="3 3"/>
          
          <line x1="26" y1="26" x2="154" y2="154" stroke="#cbd5e1" stroke-width="2.5" stroke-linecap="round"/>
          <line x1="154" y1="26" x2="26" y2="154" stroke="#cbd5e1" stroke-width="2.5" stroke-linecap="round"/>
        </svg>

        
        <div class="diamond-cell cell-top" id="cellProduct" title="Product = c = p × q">
          <span class="tag-label tag-top">Product: c = p × q</span>
          <span class="val-math tag-top" id="topVal"></span>
        </div>

        
        <div class="diamond-cell cell-bottom" id="cellSum" title="Sum = b = p + q">
          <span class="tag-label tag-bottom">Sum: b = p + q</span>
          <span class="val-math tag-bottom" id="bottomVal"></span>
        </div>

        
        <div class="diamond-cell cell-left" id="cellP" title="Factor p">
          <span class="tag-label tag-left">p</span>
          <span class="val-math tag-left" id="leftVal"></span>
        </div>

        
        <div class="diamond-cell cell-right" id="cellQ" title="Factor q">
          <span class="tag-label tag-right">q</span>
          <span class="val-math tag-right" id="rightVal"></span>
        </div>
      </div>
    </div>

    
    <div class="model-card">
      <div class="model-title">Area Model (Expanded)</div>
      <div class="area-grid">
        
        <div></div>
        <div class="area-header hdr-x">x</div>
        <div class="area-header hdr-q" id="hdrTopQ"></div>

        
        <div class="area-header hdr-x">x</div>
        <div class="area-box box-x2" id="boxX2">
          <span>x²</span>
          <span class="box-sub">x · x</span>
        </div>
        <div class="area-box box-qx" id="boxQX">
          <span id="txtQX"></span>
          <span class="box-sub" id="txtSubQX"></span>
        </div>

        
        <div class="area-header hdr-p" id="hdrLeftP"></div>
        <div class="area-box box-px" id="boxPX">
          <span id="txtPX"></span>
          <span class="box-sub" id="txtSubPX"></span>
        </div>
        <div class="area-box box-pq" id="boxPQ">
          <span id="txtPQ"></span>
          <span class="box-sub" id="txtSubPQ"></span>
        </div>
      </div>
    </div>

  </div>

  
  <div class="controls" role="group" aria-label="Example Trinomials">
    <button class="btn-preset active" data-idx="0" id="btn0"></button>
    <button class="btn-preset" data-idx="1" id="btn1"></button>
    <button class="btn-preset" data-idx="2" id="btn2"></button>
  </div>

  <script>
    const presets = [
      { b: 5, c: 6, p: 2, q: 3 },
      { b: 7, c: 12, p: 3, q: 4 },
      { b: 8, c: 15, p: 3, q: 5 }
    ];

    function render(idx) {
      const { b, c, p, q } = presets[idx];

      // Top Equation Bar
      const eqBar = document.getElementById('eqBar');
      eqBar.innerHTML = `
        <span class="eq-part">x²&nbsp;+&nbsp;<span class="term-b">${b}x</span>&nbsp;+&nbsp;<span class="term-c">${c}</span></span>
        <span class="eq-part">&nbsp;=&nbsp;</span>
        <span class="eq-part">(x&nbsp;+&nbsp;<span class="term-p">${p}</span>)(x&nbsp;+&nbsp;<span class="term-q">${q}</span>)</span>
      `;

      // Diamond Values
      document.getElementById('topVal').innerHTML = `${c} <span class="val-sub">(${p} × ${q})</span>`;
      document.getElementById('bottomVal').innerHTML = `${b} <span class="val-sub">(${p} + ${q})</span>`;
      document.getElementById('leftVal').innerHTML = `+${p}`;
      document.getElementById('rightVal').innerHTML = `+${q}`;

      // Area Model Headers & Content
      document.getElementById('hdrTopQ').textContent = `+${q}`;
      document.getElementById('hdrLeftP').textContent = `+${p}`;

      document.getElementById('txtQX').textContent = `${q}x`;
      document.getElementById('txtSubQX').textContent = `x · ${q}`;

      document.getElementById('txtPX').textContent = `${p}x`;
      document.getElementById('txtSubPX').textContent = `${p} · x`;

      document.getElementById('txtPQ').textContent = `${c}`;
      document.getElementById('txtSubPQ').textContent = `${p} · ${q}`;

      // Preset Buttons
      presets.forEach((preset, i) => {
        const btn = document.getElementById(`btn${i}`);
        btn.innerHTML = `x² + ${preset.b}x + ${preset.c}`;
        btn.classList.toggle('active', i === idx);
      });
    }

    // Set preset button event listeners
    presets.forEach((_, i) => {
      document.getElementById(`btn${i}`).addEventListener('click', () => render(i));
    });

    // Cross-highlighting between Diamond & Area Model
    function clearHighlights() {
      document.querySelectorAll('.highlight-active').forEach(el => el.classList.remove('highlight-active'));
    }

    function linkHover(triggerId, targetIds) {
      const trigger = document.getElementById(triggerId);
      if (!trigger) return;
      trigger.addEventListener('mouseenter', () => {
        targetIds.forEach(id => document.getElementById(id)?.classList.add('highlight-active'));
      });
      trigger.addEventListener('mouseleave', clearHighlights);
    }

    // Link interactions
    linkHover('cellProduct', ['cellProduct', 'boxPQ']);
    linkHover('boxPQ', ['cellProduct', 'boxPQ']);

    linkHover('cellSum', ['cellSum', 'boxPX', 'boxQX']);
    linkHover('boxPX', ['cellSum', 'boxPX']);
    linkHover('boxQX', ['cellSum', 'boxQX']);

    linkHover('cellP', ['cellP', 'hdrLeftP', 'boxPX']);
    linkHover('cellQ', ['cellQ', 'hdrTopQ', 'boxQX']);

    // Initial render
    render(0);
  </script>
</body>
</html>

Solving Monic Quadratic Equations Using the Zero-Product Property

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      user-select: none;
      max-width: 540px;
      margin: 0 auto;
    }

    .header-eq {
      text-align: center;
      font-size: 18px;
      font-weight: 700;
      color: #334155;
      padding: 4px 0 2px;
      letter-spacing: 0.5px;
      white-space: nowrap;
    }

    .header-eq span.c-var { color: #0284c7; }
    .header-eq span.b-var { color: #7c3aed; }
    .header-eq span.sym { color: #e11d48; }

    .rows-container {
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .sign-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      padding: 9px 12px;
      cursor: pointer;
      transition: border-color 0.15s ease, background-color 0.15s ease, box-shadow 0.15s ease;
    }

    .sign-row:hover {
      border-color: #cbd5e1;
      background: #f8fafc;
    }

    .sign-row.active {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.12);
    }

    .conditions {
      display: flex;
      gap: 5px;
      align-items: center;
      flex-shrink: 0;
    }

    .badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 3px 7px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 700;
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      white-space: nowrap;
    }

    .badge-c { background: #e0f2fe; color: #0369a1; }
    .badge-b { background: #ede9fe; color: #6d28d9; }
    .badge-neg { background: #fee2e2; color: #b91c1c; }

    .arrow {
      color: #94a3b8;
      font-size: 14px;
      font-weight: bold;
      flex-shrink: 0;
    }

    .result {
      display: flex;
      align-items: center;
      gap: 6px;
      justify-content: flex-end;
      flex-wrap: wrap;
      text-align: right;
    }

    .factor-badge {
      display: inline-flex;
      align-items: center;
      padding: 4px 8px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 800;
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      white-space: nowrap;
      flex-shrink: 0;
    }

    .pos-pos { background: #dcfce7; color: #15803d; border: 1px solid #bbf7d0; }
    .neg-neg { background: #ffedd5; color: #c2410c; border: 1px solid #fed7aa; }
    .pos-neg { background: #f1f5f9; color: #334155; border: 1px solid #cbd5e1; }

    .sub-note {
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      white-space: nowrap;
      line-height: 1.2;
    }

    .preview-box {
      background: #ffffff;
      border: 1.5px dashed #cbd5e1;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
    }

    .preview-label {
      font-size: 11px;
      font-weight: 800;
      text-transform: uppercase;
      letter-spacing: 0.6px;
      color: #64748b;
      background: #f1f5f9;
      padding: 3px 6px;
      border-radius: 4px;
      white-space: nowrap;
      flex-shrink: 0;
    }

    .preview-math {
      font-size: 15px;
      font-weight: 700;
      color: #0f172a;
      font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace;
      white-space: nowrap;
      overflow-x: auto;
      text-align: right;
    }

    @media (max-width: 400px) {
      body {
        padding: 8px;
        gap: 8px;
      }

      .header-eq {
        font-size: 16px;
        padding: 2px 0;
      }

      .sign-row {
        padding: 8px 10px;
      }

      .badge {
        font-size: 11px;
        padding: 3px 5px;
      }

      .factor-badge {
        font-size: 12px;
        padding: 3px 6px;
      }

      .sub-note {
        font-size: 10px;
      }

      .preview-box {
        flex-direction: column;
        align-items: flex-start;
        gap: 6px;
        padding: 8px 12px;
      }

      .preview-math {
        font-size: 13.5px;
        text-align: left;
        width: 100%;
      }
    }

    @media (max-width: 340px) {
      .result {
        flex-direction: column;
        align-items: flex-end;
        gap: 2px;
      }
    }
  </style>
</head>
<body>

  <div class="header-eq">
    x² + <span class="b-var">b</span>x + <span class="c-var">c</span> = (x <span class="sym" id="eq-s1">+</span> p)(x <span class="sym" id="eq-s2">+</span> q)
  </div>

  <div class="rows-container">
    
    <div class="sign-row active" onclick="selectRow(0)">
      <div class="conditions">
        <span class="badge badge-c">c &gt; 0</span>
        <span class="badge badge-b">b &gt; 0</span>
      </div>
      <span class="arrow">→</span>
      <div class="result">
        <span class="factor-badge pos-pos">( + ) ( + )</span>
      </div>
    </div>

    
    <div class="sign-row" onclick="selectRow(1)">
      <div class="conditions">
        <span class="badge badge-c">c &gt; 0</span>
        <span class="badge badge-neg">b &lt; 0</span>
      </div>
      <span class="arrow">→</span>
      <div class="result">
        <span class="factor-badge neg-neg">( − ) ( − )</span>
      </div>
    </div>

    
    <div class="sign-row" onclick="selectRow(2)">
      <div class="conditions">
        <span class="badge badge-neg">c &lt; 0</span>
      </div>
      <span class="arrow">→</span>
      <div class="result">
        <span class="factor-badge pos-neg">( + ) ( − )</span>
        <span class="sub-note">|larger| = sign of b</span>
      </div>
    </div>
  </div>

  <div class="preview-box">
    <span class="preview-label">Example</span>
    <span class="preview-math" id="previewMath">x² + 5x + 6 = (x + 2)(x + 3)</span>
  </div>

  <script>
    const examples = [
      {
        s1: "+", s2: "+",
        math: "x² + 5x + 6 = (x + 2)(x + 3)"
      },
      {
        s1: "−", s2: "−",
        math: "x² − 5x + 6 = (x − 2)(x − 3)"
      },
      {
        s1: "+", s2: "−",
        math: "x² + x − 6 = (x + 3)(x − 2)"
      }
    ];

    function selectRow(index) {
      const rows = document.querySelectorAll('.sign-row');
      rows.forEach((r, i) => {
        r.classList.toggle('active', i === index);
      });

      const data = examples[index];
      document.getElementById('eq-s1').textContent = data.s1;
      document.getElementById('eq-s2').textContent = data.s2;
      document.getElementById('previewMath').innerHTML = data.math;
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Solving Incomplete Quadratic Equations</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 8px 6px;
      display: flex;
      justify-content: center;
      align-items: center;
      min-height: 100%;
    }

    .math {
      font-family: "Cambria Math", "Times New Roman", Times, serif;
      font-style: italic;
    }

    .math-normal {
      font-style: normal;
    }

    .flow-container {
      display: flex;
      width: 100%;
      max-width: 620px;
      position: relative;
      gap: 12px;
    }

    .divider {
      width: 1px;
      border-left: 2px dashed #cbd5e1;
      margin: 32px 0 10px 0;
    }

    .column {
      flex: 1;
      display: flex;
      flex-direction: column;
      align-items: center;
      min-width: 0;
    }

    /* Header Badges */
    .top-badge {
      font-size: 13px;
      font-weight: 700;
      padding: 6px 14px;
      border-radius: 9999px;
      text-align: center;
      margin-bottom: 12px;
      letter-spacing: -0.01em;
      white-space: nowrap;
    }

    .badge-blue {
      background-color: #e0f2fe;
      color: #0369a1;
      border: 1px solid #bae6fd;
    }

    .badge-teal {
      background-color: #ccfbf1;
      color: #0f766e;
      border: 1px solid #99f6e4;
    }

    /* Equation Boxes */
    .step-box {
      width: 100%;
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 8px;
      text-align: center;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.04);
      transition: border-color 0.2s, box-shadow 0.2s;
    }

    .step-box:hover {
      border-color: #cbd5e1;
      box-shadow: 0 3px 6px rgba(0, 0, 0, 0.06);
    }

    .main-math {
      font-size: 19px;
      font-weight: 600;
      color: #1e2945;
      line-height: 1.2;
    }

    .example-math {
      font-size: 13px;
      color: #64748b;
      margin-top: 3px;
    }

    /* Transition Connectors */
    .transition-step {
      display: flex;
      flex-direction: column;
      align-items: center;
      width: 100%;
      margin: 3px 0;
    }

    .transition-pill {
      font-size: 11px;
      font-weight: 600;
      padding: 3px 10px;
      border-radius: 6px;
      background: #f1f5f9;
      color: #475569;
      border: 1px solid #e2e8f0;
      text-align: center;
      line-height: 1.3;
      z-index: 1;
    }

    .arrow-icon {
      width: 14px;
      height: 16px;
      color: #94a3b8;
      display: block;
      margin: 1px 0;
    }

    /* Solution Highlighting */
    .solution-box-blue {
      background-color: #f0f9ff;
      border: 2px solid #38bdf8;
      border-radius: 12px;
      box-shadow: 0 2px 6px rgba(56, 189, 248, 0.15);
    }

    .solution-box-teal {
      background-color: #f0fdfa;
      border: 2px solid #2dd4bf;
      border-radius: 12px;
      box-shadow: 0 2px 6px rgba(45, 212, 191, 0.15);
    }

    .sol-label {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.05em;
      margin-bottom: 2px;
    }

    .sol-label-blue { color: #0284c7; }
    .sol-label-teal { color: #0d9488; }

    @media (max-width: 480px) {
      .top-badge {
        font-size: 11.5px;
        padding: 5px 8px;
      }
      .main-math {
        font-size: 16px;
      }
      .example-math {
        font-size: 11.5px;
      }
      .transition-pill {
        font-size: 10px;
        padding: 2px 6px;
      }
      .flow-container {
        gap: 6px;
      }
    }
  </style>
</head>
<body>

  <div class="flow-container">
    
    
    <div class="column">
      <div class="top-badge badge-blue">
        Missing Constant (<span class="math">c</span> = 0)
      </div>

      
      <div class="step-box">
        <div class="main-math">
          <span class="math">x</span>² + <span class="math">bx</span> = 0
        </div>
        <div class="example-math">
          e.g., <span class="math">x</span>² + 6<span class="math">x</span> = 0
        </div>
      </div>

      
      <div class="transition-step">
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
        <div class="transition-pill">Factor out GCF (<span class="math">x</span>)</div>
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
      </div>

      
      <div class="step-box">
        <div class="main-math">
          <span class="math">x</span>(<span class="math">x</span> + <span class="math">b</span>) = 0
        </div>
        <div class="example-math">
          <span class="math">x</span>(<span class="math">x</span> + 6) = 0
        </div>
      </div>

      
      <div class="transition-step">
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
        <div class="transition-pill">Zero-Product Property</div>
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
      </div>

      
      <div class="step-box solution-box-blue">
        <div class="sol-label sol-label-blue">Solutions</div>
        <div class="main-math" style="color: #0369a1;">
          <span class="math">x</span> = 0 <span class="math-normal" style="font-size:14px; font-weight:500; color:#64748b;">or</span> <span class="math">x</span> = −<span class="math">b</span>
        </div>
        <div class="example-math" style="color: #0284c7; font-weight: 500;">
          <span class="math">x</span> = 0, −6
        </div>
      </div>
    </div>

    
    <div class="divider"></div>

    
    <div class="column">
      <div class="top-badge badge-teal">
        Missing Linear Term (<span class="math">b</span> = 0)
      </div>

      
      <div class="step-box">
        <div class="main-math">
          <span class="math">x</span>² − <span class="math">d</span>² = 0
        </div>
        <div class="example-math">
          e.g., <span class="math">x</span>² − 9 = 0
        </div>
      </div>

      
      <div class="transition-step">
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
        <div class="transition-pill">Difference of Squares</div>
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
      </div>

      
      <div class="step-box">
        <div class="main-math">
          (<span class="math">x</span> − <span class="math">d</span>)(<span class="math">x</span> + <span class="math">d</span>) = 0
        </div>
        <div class="example-math">
          (<span class="math">x</span> − 3)(<span class="math">x</span> + 3) = 0
        </div>
      </div>

      
      <div class="transition-step">
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
        <div class="transition-pill">Zero-Product Property</div>
        <svg class="arrow-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round">
          <line x1="12" y1="2" x2="12" y2="18"></line>
          <polyline points="6 12 12 18 18 12"></polyline>
        </svg>
      </div>

      
      <div class="step-box solution-box-teal">
        <div class="sol-label sol-label-teal">Solutions</div>
        <div class="main-math" style="color: #0f766e;">
          <span class="math">x</span> = <span class="math">d</span> <span class="math-normal" style="font-size:14px; font-weight:500; color:#64748b;">or</span> <span class="math">x</span> = −<span class="math">d</span>
        </div>
        <div class="example-math" style="color: #0d9488; font-weight: 500;">
          <span class="math">x</span> = 3, −3
        </div>
      </div>
    </div>

  </div>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Zero-Product Property</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
      user-select: none;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 16px 12px;
    }

    .diagram-area {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    /* Equation Top Card */
    .top-card {
      background: #f8fafc;
      border: 2px solid #e2e8f0;
      border-radius: 16px;
      padding: 12px 28px;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 26px;
      font-weight: 700;
      color: #1e2945;
      box-shadow: 0 4px 12px rgba(30, 41, 69, 0.05);
      z-index: 2;
    }

    .term-a {
      color: #2563eb;
      background: #eff6ff;
      padding: 2px 10px;
      border-radius: 8px;
      border: 1px solid #bfdbfe;
    }

    .term-b {
      color: #0d9488;
      background: #f0fdfa;
      padding: 2px 10px;
      border-radius: 8px;
      border: 1px solid #99f6e4;
    }

    .op {
      color: #64748b;
      font-size: 22px;
    }

    .result-zero {
      color: #1e2945;
    }

    /* SVG Connecting Arrows */
    .branch-svg {
      width: 100%;
      height: 70px;
      margin: -4px 0 -4px 0;
      display: block;
      z-index: 1;
    }

    /* Bottom Outcomes Row */
    .outcomes-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      gap: 12px;
      position: relative;
      z-index: 2;
    }

    .outcome-card {
      flex: 1;
      padding: 16px 12px;
      border-radius: 14px;
      text-align: center;
      cursor: pointer;
      transition: box-shadow 0.2s ease, border-color 0.2s ease;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }

    .outcome-a {
      background: #eff6ff;
      border: 2px solid #bfdbfe;
      color: #1e40af;
    }

    .outcome-a.active, .outcome-a:hover {
      border-color: #2563eb;
      box-shadow: 0 0 0 3px rgba(37, 99, 235, 0.2);
    }

    .outcome-b {
      background: #f0fdfa;
      border: 2px solid #99f6e4;
      color: #115e59;
    }

    .outcome-b.active, .outcome-b:hover {
      border-color: #0d9488;
      box-shadow: 0 0 0 3px rgba(13, 148, 136, 0.2);
    }

    .outcome-eq {
      font-size: 24px;
      font-weight: 700;
    }

    .outcome-sub {
      font-size: 13px;
      font-weight: 600;
      opacity: 0.85;
      font-family: monospace;
    }

    /* OR Badge */
    .or-badge {
      background: #1e2945;
      color: #ffffff;
      font-size: 13px;
      font-weight: 800;
      letter-spacing: 0.5px;
      padding: 6px 12px;
      border-radius: 20px;
      box-shadow: 0 2px 8px rgba(30, 41, 69, 0.15);
      flex-shrink: 0;
    }

    /* Live Check Box */
    .verification-bar {
      margin-top: 20px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 16px;
      font-size: 15px;
      font-weight: 600;
      color: #475569;
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .check-icon {
      color: #16a34a;
      font-weight: 800;
    }

    @media (max-width: 380px) {
      .top-card {
        font-size: 22px;
        padding: 10px 18px;
      }
      .outcome-eq {
        font-size: 20px;
      }
      .outcome-card {
        padding: 12px 8px;
      }
      .or-badge {
        padding: 4px 8px;
        font-size: 11px;
      }
    }
  </style>
</head>
<body>

  <div class="diagram-area">
    
    <div class="top-card" id="topCard">
      <span class="term-a" id="displayA">A</span>
      <span class="op">×</span>
      <span class="term-b" id="displayB">B</span>
      <span class="op">=</span>
      <span class="result-zero">0</span>
    </div>

    
    <svg class="branch-svg" viewBox="0 0 400 70" preserveAspectRatio="none">
      <defs>
        <marker id="arrow-blue" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#2563eb" />
        </marker>
        <marker id="arrow-teal" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#0d9488" />
        </marker>
      </defs>
      
      <path d="M 200 6 C 200 35, 100 25, 100 58" fill="none" stroke="#2563eb" stroke-width="3" stroke-linecap="round" marker-end="url(#arrow-blue)" />
      
      <path d="M 200 6 C 200 35, 300 25, 300 58" fill="none" stroke="#0d9488" stroke-width="3" stroke-linecap="round" marker-end="url(#arrow-teal)" />
    </svg>

    
    <div class="outcomes-row">
      <div class="outcome-card outcome-a active" id="cardA">
        <div class="outcome-eq">A = 0</div>
        <div class="outcome-sub">(0) × B = 0</div>
      </div>

      <div class="or-badge">OR</div>

      <div class="outcome-card outcome-b" id="cardB">
        <div class="outcome-eq">B = 0</div>
        <div class="outcome-sub">A × (0) = 0</div>
      </div>
    </div>

    
    <div class="verification-bar" id="statusText">
      <span class="check-icon">✓</span>
      <span id="explanation">If A = 0, the entire product is 0</span>
    </div>
  </div>

  <script>
    const cardA = document.getElementById('cardA');
    const cardB = document.getElementById('cardB');
    const displayA = document.getElementById('displayA');
    const displayB = document.getElementById('displayB');
    const explanation = document.getElementById('explanation');

    function selectLeft() {
      cardA.classList.add('active');
      cardB.classList.remove('active');
      displayA.textContent = '0';
      displayB.textContent = 'B';
      explanation.textContent = 'If A = 0, the entire product is 0';
    }

    function selectRight() {
      cardB.classList.add('active');
      cardA.classList.remove('active');
      displayA.textContent = 'A';
      displayB.textContent = '0';
      explanation.textContent = 'If B = 0, the entire product is 0';
    }

    cardA.addEventListener('click', selectLeft);
    cardB.addEventListener('click', selectRight);

    // Initial state demonstration cycle
    selectLeft();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 10px 8px;
      gap: 8px;
      user-select: none;
      min-height: 100%;
    }

    :root {
      --a-color: #0284c7;
      --a-bg: #e0f2fe;
      --a-border: #7dd3fc;
      --b-color: #7c3aed;
      --b-bg: #ede9fe;
      --b-border: #c4b5fd;
      --c-color: #059669;
      --c-bg: #d1fae5;
      --c-border: #6ee7b7;
      --accent: #2563eb;
      --accent-hover: #1d4ed8;
    }

    sup {
      font-size: 0.72em;
      line-height: 0;
      position: relative;
      vertical-align: baseline;
      top: -0.45em;
    }

    /* Equation header */
    .header-area {
      text-align: center;
      width: 100%;
      display: flex;
      justify-content: center;
    }
    .eq-badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 3px;
      font-size: 1.2rem;
      font-weight: 700;
      color: #0f172a;
      background: #ffffff;
      padding: 5px 14px;
      border-radius: 20px;
      border: 1.5px solid #e2e8f0;
      box-shadow: 0 1px 2px rgba(0,0,0,0.03);
    }

    /* Main display viewport */
    .viewport {
      position: relative;
      width: 100%;
      max-width: 520px;
      height: 200px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .step-card {
      position: absolute;
      inset: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 4px 6px;
      opacity: 0;
      visibility: hidden;
      transition: opacity 0.2s ease, visibility 0.2s ease;
    }
    .step-card.active {
      opacity: 1;
      visibility: visible;
    }

    .step-title {
      font-size: 0.8rem;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.05em;
      color: #64748b;
      margin-bottom: 8px;
    }

    /* Math typography */
    .math {
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 1.25rem;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      line-height: 1.1;
      color: #0f172a;
    }
    .math-sm {
      font-size: 1.05rem;
    }
    .math-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      margin: 2px 0;
      flex-wrap: wrap;
    }

    /* Fraction rendering */
    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      margin: 0 2px;
      font-size: 0.95em;
    }
    .num {
      border-bottom: 1.6px solid #0f172a;
      padding: 0 3px 2px 3px;
      display: inline-block;
    }
    .den {
      padding: 2px 3px 0 3px;
      display: inline-block;
    }

    /* Square root rendering */
    .sqrt {
      display: inline-flex;
      align-items: stretch;
      margin-left: 2px;
    }
    .rad-symbol {
      font-size: 1.25em;
      line-height: 0.9;
      transform: translateY(1px);
      margin-right: -1px;
    }
    .radicand {
      border-top: 1.6px solid #0f172a;
      padding: 1px 3px 0 2px;
      display: inline-flex;
      align-items: center;
    }

    /* Highlight slots */
    .slot {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 1px 5px;
      border-radius: 5px;
      font-weight: 700;
      font-family: system-ui, -apple-system, sans-serif;
      font-size: 0.88em;
      line-height: 1.1;
      margin: 0 1px;
    }
    .slot-a { background: var(--a-bg); color: var(--a-color); border: 1.5px solid var(--a-border); }
    .slot-b { background: var(--b-bg); color: var(--b-color); border: 1.5px solid var(--b-border); }
    .slot-c { background: var(--c-bg); color: var(--c-color); border: 1.5px solid var(--c-border); }

    /* Step 1 coefficient badges */
    .coef-grid {
      display: flex;
      gap: 10px;
      margin-top: 10px;
    }
    .coef-chip {
      padding: 6px 12px;
      border-radius: 8px;
      font-weight: 700;
      font-size: 1.05rem;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
      box-shadow: 0 1px 2px rgba(0,0,0,0.03);
    }
    .chip-a { background: var(--a-bg); color: var(--a-color); border: 1.5px solid var(--a-border); }
    .chip-b { background: var(--b-bg); color: var(--b-color); border: 1.5px solid var(--b-border); }
    .chip-c { background: var(--c-bg); color: var(--c-color); border: 1.5px solid var(--c-border); }
    .chip-sub {
      font-size: 0.7rem;
      opacity: 0.85;
      font-weight: 600;
      text-transform: uppercase;
      font-family: system-ui, sans-serif;
    }

    /* Step breakdown highlights */
    .calc-explain {
      display: flex;
      gap: 6px;
      margin-top: 8px;
      font-size: 0.78rem;
      color: #475569;
      flex-wrap: wrap;
      justify-content: center;
    }
    .pill-note {
      background: #f1f5f9;
      padding: 3px 8px;
      border-radius: 10px;
      border: 1px solid #e2e8f0;
      font-weight: 500;
    }
    .pill-note strong {
      color: #0f172a;
    }

    /* Branch solutions (Step 5) */
    .branch-row {
      display: flex;
      gap: 10px;
      width: 100%;
      justify-content: center;
    }
    .branch-box {
      flex: 1;
      max-width: 220px;
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      padding: 8px 6px;
      text-align: center;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }
    .branch-box.sol1 { border-color: #93c5fd; background: #f0f7ff; }
    .branch-box.sol2 { border-color: #86efac; background: #f0fdf4; }
    .branch-tag {
      font-size: 0.7rem;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.04em;
    }
    .sol1 .branch-tag { color: #0369a1; }
    .sol2 .branch-tag { color: #15803d; }
    .sol-final {
      font-size: 1.15rem;
      font-weight: 800;
      color: #0f172a;
      background: #ffffff;
      padding: 3px 10px;
      border-radius: 6px;
      border: 1.5px solid #cbd5e1;
    }

    /* Stepper navigation bar */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      width: 100%;
      flex-wrap: wrap;
    }
    .step-btn {
      padding: 5px 12px;
      border: 1.5px solid #cbd5e1;
      background: #ffffff;
      border-radius: 8px;
      font-size: 0.85rem;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
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      justify-content: center;
      min-height: 32px;
      transition: background 0.15s, border-color 0.15s;
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    .step-btn:active {
      background: #e2e8f0;
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      background: var(--accent);
      color: #ffffff;
      border-color: var(--accent);
    }
    .step-btn.primary:active {
      background: var(--accent-hover);
    }
    .step-pills {
      display: flex;
      gap: 5px;
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      border-radius: 50%;
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      font-size: 0.82rem;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      border: none;
      transition: background 0.15s, color 0.15s;
    }
    .pill.active {
      background: var(--accent);
      color: #ffffff;
      box-shadow: 0 0 0 2px #bfdbfe;
    }

    @media (max-width: 420px) {
      body { gap: 6px; padding: 6px 4px; }
      .eq-badge { font-size: 1.05rem; padding: 4px 10px; }
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      .sol-final { font-size: 1.05rem; }
      .pill-note { font-size: 0.72rem; padding: 2px 6px; }
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      .step-btn { padding: 4px 10px; font-size: 0.8rem; min-height: 28px; }
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<body>

  
  <div class="header-area">
    <div class="eq-badge math">
      <span class="slot slot-a">2</span><i>x</i><sup>2</sup>
      <span style="margin: 0 1px;">−</span>
      <span class="slot slot-b">5</span><i>x</i>
      <span style="margin: 0 1px;">−</span>
      <span class="slot slot-c">3</span>
      <span style="margin-left: 2px;">= 0</span>
    </div>
  </div>

  
  <div class="viewport">

    
    <div class="step-card active" id="card-0">
      <div class="step-title">Step 1 • Identify Coefficients</div>
      <div class="math"><i>a</i><i>x</i><sup>2</sup> + <i>b</i><i>x</i> + <i>c</i> = 0</div>
      <div class="coef-grid">
        <div class="coef-chip chip-a">
          <span>a = 2</span>
          <span class="chip-sub"><i>x</i><sup>2</sup> term</span>
        </div>
        <div class="coef-chip chip-b">
          <span>b = −5</span>
          <span class="chip-sub"><i>x</i> term</span>
        </div>
        <div class="coef-chip chip-c">
          <span>c = −3</span>
          <span class="chip-sub">constant</span>
        </div>
      </div>
    </div>

    
    <div class="step-card" id="card-1">
      <div class="step-title">Step 2 • Substitute Values</div>
      <div class="math math-sm" style="margin-bottom: 6px; color: #475569;">
        <i>x</i> = 
        <span class="frac">
          <span class="num">−<i>b</i> ± <span class="sqrt"><span class="rad-symbol">√</span><span class="radicand"><i>b</i><sup>2</sup> − 4<i>a</i><i>c</i></span></span></span>
          <span class="den">2<i>a</i></span>
        </span>
      </div>
      <div class="math">
        <i>x</i> = 
        <span class="frac">
          <span class="num">
            −(<span class="slot slot-b">−5</span>) ± 
            <span class="sqrt">
              <span class="rad-symbol">√</span>
              <span class="radicand">(<span class="slot slot-b">−5</span>)<sup>2</sup> − 4(<span class="slot slot-a">2</span>)(<span class="slot slot-c">−3</span>)</span>
            </span>
          </span>
          <span class="den">2(<span class="slot slot-a">2</span>)</span>
        </span>
      </div>
    </div>

    
    <div class="step-card" id="card-2">
      <div class="step-title">Step 3 • Simplify Under Radical</div>
      <div class="math">
        <i>x</i> = 
        <span class="frac">
          <span class="num">5 ± <span class="sqrt"><span class="rad-symbol">√</span><span class="radicand">25 + 24</span></span></span>
          <span class="den">4</span>
        </span>
      </div>
      <div class="calc-explain">
        <div class="pill-note">−(−5) = <strong>5</strong></div>
        <div class="pill-note">(−5)<sup>2</sup> = <strong>25</strong></div>
        <div class="pill-note">−4(2)(−3) = <strong>+24</strong></div>
        <div class="pill-note">2(2) = <strong>4</strong></div>
      </div>
    </div>

    
    <div class="step-card" id="card-3">
      <div class="step-title">Step 4 • Calculate Square Root</div>
      <div class="math math-row">
        <i>x</i> = 
        <span class="frac">
          <span class="num">5 ± <span class="sqrt"><span class="rad-symbol">√</span><span class="radicand">49</span></span></span>
          <span class="den">4</span>
        </span>
        <span style="margin: 0 4px;">=</span>
        <span class="frac">
          <span class="num">5 ± 7</span>
          <span class="den">4</span>
        </span>
      </div>
      <div class="calc-explain">
        <div class="pill-note"><span class="sqrt"><span class="rad-symbol" style="font-size:1.1em;">√</span><span class="radicand">49</span></span> = <strong>7</strong></div>
      </div>
    </div>

    
    <div class="step-card" id="card-4">
      <div class="step-title">Step 5 • Split Into Two Branches</div>
      <div class="branch-row">
        
        <div class="branch-box sol1">
          <div class="branch-tag">Plus (+) Branch</div>
          <div class="math math-sm">
            <i>x</i> = 
            <span class="frac">
              <span class="num">5 + 7</span>
              <span class="den">4</span>
            </span>
            = 
            <span class="frac">
              <span class="num">12</span>
              <span class="den">4</span>
            </span>
          </div>
          <div class="sol-final"><i>x</i> = 3</div>
        </div>

        
        <div class="branch-box sol2">
          <div class="branch-tag">Minus (−) Branch</div>
          <div class="math math-sm">
            <i>x</i> = 
            <span class="frac">
              <span class="num">5 − 7</span>
              <span class="den">4</span>
            </span>
            = 
            <span class="frac">
              <span class="num">−2</span>
              <span class="den">4</span>
            </span>
          </div>
          <div class="sol-final">
            <i>x</i> = −<span class="frac"><span class="num">1</span><span class="den">2</span></span>
          </div>
        </div>
      </div>
    </div>

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Using the Quadratic Formula to Solve Equations

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      font-weight: 700;
      color: #1e293b;
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      flex: 1;
      padding: 10px 8px;
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      border-radius: 8px;
      font-size: 14px;
      font-weight: 600;
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      transition: background 0.15s ease, border-color 0.15s ease, color 0.15s ease;
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      background: #f1f5f9;
    }
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      background: #eff6ff;
      border-color: #2563eb;
      color: #1d4ed8;
      box-shadow: 0 1px 3px rgba(37, 99, 235, 0.15);
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    .panel {
      display: none;
      flex-direction: column;
      gap: 12px;
      width: 100%;
    }
    .panel.active {
      display: flex;
    }
    .compare-card {
      border-radius: 10px;
      padding: 14px 16px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      box-shadow: 0 1px 2px rgba(0, 0, 0, 0.04);
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    .card-wrong {
      background: #fff5f5;
      border: 1.5px solid #fca5a5;
    }
    .card-correct {
      background: #f0fdf4;
      border: 1.5px solid #86efac;
    }
    .card-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
    }
    .card-badge {
      display: inline-flex;
      align-items: center;
      gap: 5px;
      font-size: 13px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
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    .card-wrong .card-badge {
      color: #b91c1c;
    }
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      color: #15803d;
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    .badge-icon {
      font-size: 15px;
      width: 20px;
      height: 20px;
      border-radius: 50%;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      color: #ffffff;
    }
    .card-wrong .badge-icon {
      background: #ef4444;
    }
    .card-correct .badge-icon {
      background: #22c55e;
    }
    .note-pill {
      font-size: 12px;
      font-weight: 600;
      padding: 3px 10px;
      border-radius: 999px;
    }
    .note-wrong {
      background: #fee2e2;
      color: #991b1b;
      border: 1px solid #fecaca;
    }
    .note-correct {
      background: #dcfce7;
      color: #166534;
      border: 1px solid #bbf7d0;
    }
    .math-row {
      display: flex;
      align-items: center;
      justify-content: center;
      font-family: 'Cambria Math', 'Times New Roman', Cambria, Georgia, serif;
      font-size: 22px;
      padding: 6px 4px;
      color: #0f172a;
      flex-wrap: wrap;
      gap: 6px 10px;
      line-height: 1.2;
    }
    .math-math {
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }
    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      font-size: 0.9em;
      margin: 0 2px;
    }
    .num {
      border-bottom: 1.5px solid currentColor;
      padding: 0 4px 1px;
    }
    .den {
      padding: 1px 4px 0;
    }
    .sqrt {
      display: inline-flex;
      align-items: center;
      margin-left: 1px;
    }
    .sqrt-sym {
      font-style: normal;
      font-size: 1.1em;
      line-height: 1;
    }
    .sqrt-rad {
      border-top: 1.5px solid currentColor;
      padding-top: 0px;
      padding-left: 1px;
      padding-right: 1px;
      display: inline-block;
      line-height: 1.1;
    }
    .strike-out {
      position: relative;
      display: inline-block;
      color: #dc2626;
      font-weight: bold;
    }
    .strike-out::after {
      content: '';
      position: absolute;
      left: -3px;
      right: -3px;
      top: 50%;
      height: 2.5px;
      background: #dc2626;
      transform: rotate(-16deg);
      border-radius: 2px;
    }
    .highlight-correct {
      color: #16a34a;
      font-weight: bold;
    }
    .cancel-slash {
      position: relative;
      display: inline-block;
      color: #dc2626;
    }
    .cancel-slash::after {
      content: '';
      position: absolute;
      left: -1px;
      right: -1px;
      top: 50%;
      height: 2px;
      background: #dc2626;
      transform: rotate(-45deg);
    }
    .explanation {
      font-size: 13.5px;
      line-height: 1.45;
      color: #334155;
      background: rgba(255, 255, 255, 0.7);
      padding: 8px 12px;
      border-radius: 6px;
    }
    .explanation strong {
      color: #0f172a;
    }
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        padding: 10px;
      }
      .tab-btn {
        font-size: 13px;
        padding: 8px 4px;
      }
      .math-row {
        font-size: 18px;
      }
      .card-header {
        flex-direction: row;
      }
    }
  </style>
</head>
<body>

  <div class="container">
    <div class="header-title">Common Quadratic Formula Mistakes</div>

    <div class="nav-tabs" role="tablist">
      <button class="tab-btn active" id="tab-0" onclick="switchTab(0)" role="tab" aria-selected="true">
        1. Squaring Negative <i>b</i>
      </button>
      <button class="tab-btn" id="tab-1" onclick="switchTab(1)" role="tab" aria-selected="false">
        2. Canceling Denominator
      </button>
    </div>

    
    <div id="panel-0" class="panel active" role="tabpanel">
      
      <div class="compare-card card-wrong">
        <div class="card-header">
          <div class="card-badge">
            <span class="badge-icon">✕</span> Common Mistake
          </div>
          <span class="note-pill note-wrong">Missing Parentheses</span>
        </div>
        <div class="math-row">
          <span>&minus;5<sup>2</sup> &nbsp;=&nbsp; &minus;(5 &times; 5) &nbsp;=&nbsp; <span class="strike-out">&minus;25</span></span>
        </div>
        <div class="explanation">
          <strong>Why it's wrong:</strong> Without parentheses, the exponent applies only to 5, keeping the negative sign in front.
        </div>
      </div>

      
      <div class="compare-card card-correct">
        <div class="card-header">
          <div class="card-badge">
            <span class="badge-icon">✓</span> Correct Execution
          </div>
          <span class="note-pill note-correct">Include ( )</span>
        </div>
        <div class="math-row">
          <span>(&minus;5)<sup>2</sup> &nbsp;=&nbsp; (&minus;5) &times; (&minus;5) &nbsp;=&nbsp; <span class="highlight-correct">+25</span></span>
        </div>
        <div class="explanation">
          <strong>Why it's correct:</strong> When substituting <i>b</i> = &minus;5 into <i>b</i><sup>2</sup>, always enclose negative values in parentheses: <i>b</i><sup>2</sup> is always &ge; 0 for real numbers.
        </div>
      </div>
    </div>

    
    <div id="panel-1" class="panel" role="tabpanel">
      
      <div class="compare-card card-wrong">
        <div class="card-header">
          <div class="card-badge">
            <span class="badge-icon">✕</span> Common Mistake
          </div>
          <span class="note-pill note-wrong">Partial Canceling</span>
        </div>
        <div class="math-row">
          <div class="math-math">
            <div class="frac">
              <span class="num"><span class="cancel-slash">4</span> &plusmn; 2<span class="sqrt"><span class="sqrt-sym">&radic;</span><span class="sqrt-rad">3</span></span></span>
              <span class="den"><span class="cancel-slash">2</span></span>
            </div>
            <span>&nbsp;&ne;&nbsp; <span class="strike-out">2 &plusmn; 2<span class="sqrt"><span class="sqrt-sym">&radic;</span><span class="sqrt-rad">3</span></span></span></span>
          </div>
        </div>
        <div class="explanation">
          <strong>Why it's wrong:</strong> You cannot divide only one term in the numerator by the denominator while leaving the other term unchanged.
        </div>
      </div>

      
      <div class="compare-card card-correct">
        <div class="card-header">
          <div class="card-badge">
            <span class="badge-icon">✓</span> Correct Execution
          </div>
          <span class="note-pill note-correct">Factor Out First</span>
        </div>
        <div class="math-row">
          <div class="math-math">
            <div class="frac">
              <span class="num">4 &plusmn; 2<span class="sqrt"><span class="sqrt-sym">&radic;</span><span class="sqrt-rad">3</span></span></span>
              <span class="den">2</span>
            </div>
            <span>&nbsp;=&nbsp;</span>
            <div class="frac">
              <span class="num">2(2 &plusmn; <span class="sqrt"><span class="sqrt-sym">&radic;</span><span class="sqrt-rad">3</span></span>)</span>
              <span class="den">2</span>
            </div>
            <span>&nbsp;=&nbsp; <span class="highlight-correct">2 &plusmn; <span class="sqrt"><span class="sqrt-sym">&radic;</span><span class="sqrt-rad">3</span></span></span></span>
          </div>
        </div>
        <div class="explanation">
          <strong>Why it's correct:</strong> Factor out the common factor <strong>2</strong> from every numerator term before canceling with the denominator.
        </div>
      </div>
    </div>
  </div>

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      width: 100%;
      max-width: 580px;
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</head>
<body>

  <div class="container">
    <div class="header">
      <div class="title">Visual Proof: Quadratic Formula</div>
    </div>

    
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      <button class="step-btn" onclick="goToStep(1)">Step 2</button>
      <button class="step-btn" onclick="goToStep(2)">Step 3</button>
      <button class="step-btn" onclick="goToStep(3)">Step 4</button>
      <button class="step-btn" onclick="goToStep(4)">Step 5</button>
      <button class="step-btn" onclick="goToStep(5)">Step 6</button>
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    <div class="stage">
      <div class="badge-row">
        <span class="step-counter" id="stepCounter">1 of 6</span>
        <div class="action-badge" id="actionBadge">Standard Form</div>
      </div>
      
      <div class="equation-container">
        <div class="prev-box" id="prevBox">
          <span class="prev-label">From:</span>
          <div id="prevEq" class="math prev-math"></div>
        </div>
        <div class="main-equation-box">
          <div class="math" id="mainEq"></div>
        </div>
      </div>

      <div class="step-desc" id="stepDesc">
        Start with the standard quadratic equation.
      </div>
    </div>

    
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      <button class="ctrl-btn" onclick="prevStep()" aria-label="Previous step">← Prev</button>
      <button class="ctrl-btn primary" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
      <button class="ctrl-btn" onclick="nextStep()" aria-label="Next step">Next →</button>
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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
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      width: 28px;
      height: 28px;
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</head>
<body class="active-a">

  <div class="eq-panel">
    
    <div class="standard-form">
      <span class="tok tok-a">a</span>x<sup>2</sup>
      <span class="tok-op">&nbsp;+&nbsp;</span>
      <span class="tok tok-b">b</span>x
      <span class="tok-op">&nbsp;+&nbsp;</span>
      <span class="tok tok-c">c</span>
      <span class="tok-op">&nbsp;=&nbsp;0</span>
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      <div class="fraction">
        <div class="numerator">
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          <span class="tok tok-pm">&nbsp;±&nbsp;</span>
          <div class="sqrt-group">
            <span class="radical">√</span>
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  </div>

  
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        else if (el.classList.contains('tok-b')) setActive('b');
        else if (el.classList.contains('tok-c')) setActive('c');
        else if (el.classList.contains('tok-pm')) setActive('pm');
      });
    });
  </script>
</body>
</html>

OGM.10.REI.2

Aligned learning resources

Related diagrams