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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 2 x^{2} + 32 x + 126=0\)
Since the GCF is \(\displaystyle 2\) we need we factor out the GCF to get \(\displaystyle 2(x^{2} + 16 x + 63)\). This is now a pq method factoring. The factors of \(\displaystyle 63\) that add up to \(\displaystyle 16\) are \(\displaystyle 9\) and \(\displaystyle 7\). This gives \(\displaystyle 2(x + 9)(x + 7)=0\). The solutions are \(\displaystyle x = -9\) and \(\displaystyle x = -7\)
\begin{question}Solve $2 x^{2} + 32 x + 126=0$
\soln{9cm}{Since the GCF is $2$ we need we factor out the GCF to get $2(x^{2} + 16 x + 63)$. This is now a pq method factoring. The factors of $63$ that add up to $16$ are $9$ and $7$. This gives $2(x + 9)(x + 7)=0$. The solutions are $x = -9$ and $x = -7$}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle 2 x^{2} + 32 x + 126=0 " src="/equation_images/%20%5Cdisplaystyle%202%20x%5E%7B2%7D%20%2B%2032%20x%20%2B%20126%3D0%20" alt="LaTeX: \displaystyle 2 x^{2} + 32 x + 126=0 " data-equation-content=" \displaystyle 2 x^{2} + 32 x + 126=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> we need we factor out the GCF to get <img class="equation_image" title=" \displaystyle 2(x^{2} + 16 x + 63) " src="/equation_images/%20%5Cdisplaystyle%202%28x%5E%7B2%7D%20%2B%2016%20x%20%2B%2063%29%20" alt="LaTeX: \displaystyle 2(x^{2} + 16 x + 63) " data-equation-content=" \displaystyle 2(x^{2} + 16 x + 63) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle 63 " src="/equation_images/%20%5Cdisplaystyle%2063%20" alt="LaTeX: \displaystyle 63 " data-equation-content=" \displaystyle 63 " /> that add up to <img class="equation_image" title=" \displaystyle 16 " src="/equation_images/%20%5Cdisplaystyle%2016%20" alt="LaTeX: \displaystyle 16 " data-equation-content=" \displaystyle 16 " /> are <img class="equation_image" title=" \displaystyle 9 " src="/equation_images/%20%5Cdisplaystyle%209%20" alt="LaTeX: \displaystyle 9 " data-equation-content=" \displaystyle 9 " /> and <img class="equation_image" title=" \displaystyle 7 " src="/equation_images/%20%5Cdisplaystyle%207%20" alt="LaTeX: \displaystyle 7 " data-equation-content=" \displaystyle 7 " /> . This gives <img class="equation_image" title=" \displaystyle 2(x + 9)(x + 7)=0 " src="/equation_images/%20%5Cdisplaystyle%202%28x%20%2B%209%29%28x%20%2B%207%29%3D0%20" alt="LaTeX: \displaystyle 2(x + 9)(x + 7)=0 " data-equation-content=" \displaystyle 2(x + 9)(x + 7)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -9 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-9%20" alt="LaTeX: \displaystyle x = -9 " data-equation-content=" \displaystyle x = -9 " /> and <img class="equation_image" title=" \displaystyle x = -7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-7%20" alt="LaTeX: \displaystyle x = -7 " data-equation-content=" \displaystyle x = -7 " /> </p> </p>