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<p><strong><em>Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<p>For questions 1 - 5, the standard form of an equation is \(ax^2+bx+c\). For each expression, find the missing constant \(c\) that would make the expression a perfect square.</p>
<ol class="os-raise-noindent">
<li>\(x^2−6x+ \underline{\;\;c\;\;}\)</li>
</ol>
<p><strong>Answer:</strong> 9</p>
<ol class="os-raise-noindent" start="2">
<li>\(x^2+2x+ \underline{\;\;c\;\;}\)</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="3">
<li>\(x^2+14x+ \underline{\;\;c\;\;}\)</li>
</ol>
<p><strong>Answer:</strong> 49</p>
<ol class="os-raise-noindent" start="4">
<li>\(x^2−4x+ \underline{\;\;c\;\;}\)</li>
</ol>
<p><strong>Answer:</strong> 4</p>
<ol class="os-raise-noindent" start="5">
<li>\(x^2+24x+ \underline{\;\;c\;\;}\)</li>
</ol>
<p><strong>Answer:</strong> 144</p>
<ol class="os-raise-noindent" start="6">
<li>If \(x^2−6x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to include the sign.</li>
</ol>
<p><strong>Answer:</strong> -3</p>
<ol class="os-raise-noindent" start="7">
<li>If \(x^2+2x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to include the sign.</li>
</ol>
<p><strong>Answer:</strong> +1</p>
<ol class="os-raise-noindent" start="8">
<li>If \(x^2+14x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
<p><strong>Answer:</strong> +7</p>
<ol class="os-raise-noindent" start="9">
<li>If \(x^2−4x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
<p><strong>Answer:</strong> -2</p>
<ol class="os-raise-noindent" start="10">
<li>If \(x^2+24x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
<p><strong>Answer:</strong> +12</p>
<p>For each equation in questions 11 - 14, use the following scenario.</p>
<blockquote>
<p>Jada looks at Mai's work and is confused. She doesn't see how Mai got her answer.</p>
<p>Complete Mai's missing steps by answering the questions to help Jada see how Mai solved the equation.</p>
</blockquote>
<p>\(x^2+12x=13\)</p>
<p><strong>Step 1 - </strong>\(x^2\;+\;12x\; +\) \(\_\_\_\_\_\) \(=\;13\;+\) \(\_\_\_\_\_\)</p>
<p><strong>Step 2 -</strong> \((x+6)^2=49\)</p>
<p><strong>Step 3 - </strong>\(\sqrt{(x+6)^2}=\sqrt{49}\)</p>
<p><strong>Step 4 -</strong> \(x+6= \pm\) \(\_\_\_\_\_\)</p>
<p><strong>Step 5 - </strong>\(x+6=\) \(\_\_\_\_\_\)</p>
<p><strong>Step 6 -</strong> \(x\;+\;6=\) \(-\) \(\_\_\_\_\_\)</p>
<p>\(x=1\) or \(x=-13\)</p>
<ol class="os-raise-noindent" start="11">
<li>What is the missing term in Step 1?</li>
</ol>
<p><strong>Answer:</strong> 36</p>
<ol class="os-raise-noindent" start="12">
<li>What is the missing term in Steps 4, 5, and 6?</li>
</ol>
<p><strong>Answer:</strong> 7</p>
<ol class="os-raise-noindent" start="13">
<li>What is the value of \(x\) in Step 5?</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="14">
<li>What is the value of \(x\) in Step 6?</li>
</ol>
<p><strong>Answer:</strong> -13</p>
<p>For questions 15 - 20, solve choose the equivalent equation with a perfect square on one side.</p>
<ol class="os-raise-noindent" start="15">
<li>\(x^2+8x=2\) </li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \((x−7)^2=54\) </li>
<li> \((x+5)^2=12\) </li>
<li> \((x−10)^2=91\) </li>
<li> \((x+4)^2=18\) </li>
<li> \((x+1)^2=1\) </li>
<li> \((x+2)^2=9\) </li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x+4)^2=18\)</p>
<ol class="os-raise-noindent" start="16">
<li>\(x^2+10x=-13\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \((x−7)^2=54\) </li>
<li> \((x+5)^2=12\)</li>
<li> \((x−10)^2=91\) </li>
<li> \((x+4)^2=18\)</li>
<li> \((x+1)^2=1\)</li>
<li> \((x+2)^2=9\)</li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x+5)^2=12\)</p>
<ol class="os-raise-noindent" start="17">
<li>\(x^2−14x=5\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \((x−7)^2=54\)</li>
<li> \((x+5)^2=12\)</li>
<li> \((x−10)^2=91\)</li>
<li> \((x+4)^2=18\)</li>
<li> \((x+1)^2=1\)</li>
<li> \((x+2)^2=9\)</li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x−7)^2=54\)</p>
<ol class="os-raise-noindent" start="18">
<li>\(x^2+2x=0\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li>\((x−7)^2=54\) </li>
<li> \((x+5)^2=12\) </li>
<li> \((x−10)^2=91\)</li>
<li> \((x+4)^2=18\)</li>
<li> \((x+1)^2=1\)</li>
<li> \((x+2)^2=9\)</li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x+1)^2=1\)</p>
<ol class="os-raise-noindent" start="19">
<li>\(x^2+4x−5=0\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \((x−7)^2=54\)</li>
<li> \((x+5)^2=12\)</li>
<li> \((x−10)^2=91\)</li>
<li> \((x+4)^2=18\)</li>
<li> \((x+1)^2=1\)</li>
<li>\((x+2)^2=9\)</li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x+2)^2=9\)</p>
<ol class="os-raise-noindent" start="20">
<li>\(x^2−20x=-9\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li>\((x−7)^2=54\)</li>
<li> \((x+5)^2=12\)</li>
<li> \((x−10)^2=91\)</li>
<li> \((x+4)^2=18\)</li>
<li> \((x+1)^2=1\)</li>
<li> \((x+2)^2=9\)</li>
</ul>
</ul>
<p><strong>Answer:</strong> \((x−10)^2=91\)</p>
<p>Solve each equation by completing the square, then choose the <strong>two</strong> roots.</p>
<ol class="os-raise-noindent" start="21">
<li>\(x^2−6x+5=12\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \(x = -1\) </li>
<li>\( x = 5\) </li>
<li> \(x = 2\) </li>
<li> \(x = 7\) </li>
<li> \(x = 6\) </li>
</ul>
</ul>
<p><strong>Answer:</strong> \(x =-1\), \(x = 7\)</p>
<ol class="os-raise-noindent" start="22">
<li>\(x^2−2x=8\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li>\(x = 9\) </li>
<li> \(x = -2\) </li>
<li> \(x = 8\) </li>
<li> \(x = 3\) </li>
<li> \(x = 4\) </li>
</ul>
</ul>
<p><strong>Answer:</strong> \(x= -2\), \(x = 4\)</p>
<ol class="os-raise-noindent" start="23">
<li>\(11=x^2+4x−1\)</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \(x = 14\) </li>
<li> \(x = 110\) </li>
<li> \(x = -6\) </li>
<li> \(x = 2\) </li>
<li> \(x = 4\) </li>
</ul>
</ul>
<p><strong>Answer:</strong> \(x = -6\), \(x = 2\)</p>
<ol class="os-raise-noindent" start="24">
<li>Solve the equation \(x^2−18x+60=-21\) by completing the square.</li>
</ol>
<ul class="os-raise-noindent">
<ul>
<li> \(x = -21\) </li>
<li>\(x = 9\) </li>
<li> \(x = 39\) </li>
<li> \(x = 78\) </li>
<li> \(x = -39\) </li>
</ul>
</ul>
<p><strong>Answer:</strong> \(x = 9\)</p>