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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 5 x^{2} + 20 x + 225=0\)
Since the GCF is \(\displaystyle -5\) we need we factor out the GCF to get \(\displaystyle -5(x^{2} - 4 x - 45)\). This is now a pq method factoring. The factors of \(\displaystyle -45\) that add up to \(\displaystyle -4\) are \(\displaystyle 5\) and \(\displaystyle -9\). This gives \(\displaystyle -5(x + 5)(x - 9)=0\). The solutions are \(\displaystyle x = -5\) and \(\displaystyle x = 9\)
\begin{question}Solve $- 5 x^{2} + 20 x + 225=0$
\soln{9cm}{Since the GCF is $-5$ we need we factor out the GCF to get $-5(x^{2} - 4 x - 45)$. This is now a pq method factoring. The factors of $-45$ that add up to $-4$ are $5$ and $-9$. This gives $-5(x + 5)(x - 9)=0$. The solutions are $x = -5$ and $x = 9$}
\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 - 5 x^{2} + 20 x + 225=0 " src="/equation_images/%20%5Cdisplaystyle%20-%205%20x%5E%7B2%7D%20%2B%2020%20x%20%2B%20225%3D0%20" alt="LaTeX: \displaystyle - 5 x^{2} + 20 x + 225=0 " data-equation-content=" \displaystyle - 5 x^{2} + 20 x + 225=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle -5 " src="/equation_images/%20%5Cdisplaystyle%20-5%20" alt="LaTeX: \displaystyle -5 " data-equation-content=" \displaystyle -5 " /> we need we factor out the GCF to get <img class="equation_image" title=" \displaystyle -5(x^{2} - 4 x - 45) " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%5E%7B2%7D%20-%204%20x%20-%2045%29%20" alt="LaTeX: \displaystyle -5(x^{2} - 4 x - 45) " data-equation-content=" \displaystyle -5(x^{2} - 4 x - 45) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -45 " src="/equation_images/%20%5Cdisplaystyle%20-45%20" alt="LaTeX: \displaystyle -45 " data-equation-content=" \displaystyle -45 " /> that add up to <img class="equation_image" title=" \displaystyle -4 " src="/equation_images/%20%5Cdisplaystyle%20-4%20" alt="LaTeX: \displaystyle -4 " data-equation-content=" \displaystyle -4 " /> are <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX: \displaystyle 5 " data-equation-content=" \displaystyle 5 " /> and <img class="equation_image" title=" \displaystyle -9 " src="/equation_images/%20%5Cdisplaystyle%20-9%20" alt="LaTeX: \displaystyle -9 " data-equation-content=" \displaystyle -9 " /> . This gives <img class="equation_image" title=" \displaystyle -5(x + 5)(x - 9)=0 " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%20%2B%205%29%28x%20-%209%29%3D0%20" alt="LaTeX: \displaystyle -5(x + 5)(x - 9)=0 " data-equation-content=" \displaystyle -5(x + 5)(x - 9)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -5 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-5%20" alt="LaTeX: \displaystyle x = -5 " data-equation-content=" \displaystyle x = -5 " /> and <img class="equation_image" title=" \displaystyle x = 9 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%209%20" alt="LaTeX: \displaystyle x = 9 " data-equation-content=" \displaystyle x = 9 " /> </p> </p>