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<h4>Solving Quadratics with Radical Solutions</h4>
<p>When solving quadratic equations, it is important to remember that:</p>
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  <li> Any positive number has two square roots, one positive and one negative, because there are two numbers that can be squared to make that number. (For example, \(6^2 \)and \((-6)^2\) both equal 36, so 6 and -6 are both square roots of 36.) </li>
  <li> The square root symbol \((\sqrt{\;\;})\) can be used to express the positive square root of a number. For example, the square root of 36 is 6, but it can also be written as \(\sqrt{36}\) because \(\sqrt{36} \cdot \sqrt{36}=36\). </li>
  <li> To express the negative square root of a number, say 36, we can write -6 or \(-\sqrt{36}\). </li>
  <li> When a number is not a perfect square (for example, 40), we can express its square roots by writing \(\sqrt{40}\) and \(-\sqrt{40}\). </li>
</ul>
<p>How could we write the solutions to an equation like \((x+4)^2=11\)? This equation is saying, &ldquo;something squared is 11.&rdquo; To make the equation true, that something must be \(\sqrt{11}\) or \(-\sqrt{11}\).</p>
<p>We can write:</p>
<p>\(x+4= \sqrt{11}\) &nbsp;&nbsp;&nbsp;&nbsp; or &nbsp;&nbsp;&nbsp;&nbsp; \(x+4= - \sqrt{11}\)</p>
<p>\(x=-4+ \sqrt{11}\) &nbsp;&nbsp;&nbsp;&nbsp; or &nbsp;&nbsp;&nbsp;&nbsp; \(x=-4+- \sqrt{11}\) </p>
<p>A more compact way to write the two solutions to the equation is: \(x=-4 \pm \sqrt{11}\).</p>
<h4>Try It: Solving Quadratics with Radical Solutions</h4>
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    <p>Solve \((x-2)^2=17\).</p>
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  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
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  <p>Here is how to solve this quadratic equation:</p>
  <p><strong>Step 1</strong> - Make sure the quadratic is isolated on one side.<br>
    \((x-2)^2=17\)</p>
  <p><strong>Step 2</strong> - Take the square root of both sides.<br>
    \(\sqrt{(x-2)^2}= \pm \sqrt{17}\)</p>
  <p><strong>Step 3</strong> - Simplify.<br>
    \(x-2= \pm \sqrt{17}\)</p>
  <p><strong>Step 4</strong> - Solve the equation. For this problem, add 2 to each side.<br>
    \(
    x-2+2=2 \pm \sqrt{17}\)</p>
  <p><strong>Step 5</strong> - Simplify.<br>
    \(x=2- \sqrt{17}\), \(x=2+ \sqrt{17}\)</p>
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