f91e56e6-74a3-4eb5-9298-abba227f4a23.html

<h4>Cool Down Activity</h4>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <p>Here is one solution for solving \(x^2+3x+8=0\) by <span class="os-raise-ib-tooltip" data-schema-version="&ldquo;1.0&rdquo;" data-store="glossary-tooltip">completing the square</span>, where each step is shown, but numerical expressions are not evaluated.</p>
    <p>Original equation<br>
      \(x^2+3x+8=0\)</p>
    <p><strong>Step 1</strong> - \(x^2+3x=-8\)</p>
    <p><strong>Step 2</strong> - \(4x^2+4(3x)=4(-8)\)</p>
    <p><strong>Step 3</strong> - \((2x)^2+6(2x)=-32\)</p>
    <p><strong>Step 4</strong> - \(P^2+6P=-32\)</p>
    <p><strong>Step 5</strong> - \(P^2+6P+3^2=-32+3^2\)</p>
    <p><strong>Step 6</strong> - \((P+3)^2=3^2-32\)</p>
    <p><strong>Step 7</strong> - \(P+3= \pm \sqrt{3^2-32}\)</p>
    <p><strong>Step 8</strong> - \(P=-3 \pm \sqrt{3^2-32}\)</p>
    <p><strong>Step 9</strong> - \(2x=-3 \pm \sqrt{3^2-32}\)</p>
    <p><strong>Step 10</strong> - <br>
      \(x= \frac{-3 \pm \sqrt{3^2-32}}{2}\)</p>
    <ol class="os-raise-noindent">
      <li>In Step 2, the equation is multiplied by 4. Why might that be?</li>
    </ol>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Compare your answer:</p>
  <p>To make the coefficient of \(x^2\) a <span class="os-raise-ib-tooltip" data-schema-version="&ldquo;1.0&rdquo;" data-store="glossary-tooltip">perfect square</span> and the coefficient of \(x\) an even number</p>
</div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <ol class="os-raise-noindent" start="2">
      <li>In Step 5, \(3^2\) is added to each side. Why might that be?</li>
    </ol>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal2">
  <p>Compare your answer:</p>
  <p>\(3^2\) completes the square for the expression on the left side. To keep the two sides equal, it needs to be added to the other side as well.</p>
</div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <ol class="os-raise-noindent" start="3">
      <li>What happened between Step 5 and Step 6?</li>
    </ol>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal3">
  <p>Compare your answer:</p>
  <p>The perfect square is rewritten in factored form, and \(-32+3^2\) is rewritten as \(3^2-32\).</p>
</div>
<br>
<div class="os-raise-student-reflection">
  <p class="os-raise-student-reflection-title">Building Character: Intellectual Humility</p>
  <div class="os-raise-d-flex-nowrap os-raise-gap-1">
    <img src="https://k12.openstax.org/contents/raise/resources/0943d627452fc6cc10570e6cded146178d40e44d"
      width="200px" height="200px"
    />
    <div>
      <p class="os-raise-mb-0">No matter how old you are, with intellectual humility you become wiser. It helps you be less judgmental of others, learn more in school, and be a better leader. </p>
      <p>Think about yourself. Are these statements true for you?</p>
      <ul>
        <li>
          I recognize the value in opinions that are different from my own. 
        </li>
        <li>
          I accept that my beliefs and attitudes may be wrong. 
        </li>
      </ul>
      <p>Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!</p>
     </div>
  </div>
</div>