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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 5 x^{2} - 80 x - 300=0\)
Since the GCF is \(\displaystyle -5\) we need we factor out the GCF to get \(\displaystyle -5(x^{2} + 16 x + 60)\). This is now a pq method factoring. The factors of \(\displaystyle 60\) that add up to \(\displaystyle 16\) are \(\displaystyle 6\) and \(\displaystyle 10\). This gives \(\displaystyle -5(x + 6)(x + 10)=0\). The solutions are \(\displaystyle x = -6\) and \(\displaystyle x = -10\)
\begin{question}Solve $- 5 x^{2} - 80 x - 300=0$
\soln{9cm}{Since the GCF is $-5$ we need we factor out the GCF to get $-5(x^{2} + 16 x + 60)$. This is now a pq method factoring. The factors of $60$ that add up to $16$ are $6$ and $10$. This gives $-5(x + 6)(x + 10)=0$. The solutions are $x = -6$ and $x = -10$}
\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} - 80 x - 300=0 " src="/equation_images/%20%5Cdisplaystyle%20-%205%20x%5E%7B2%7D%20-%2080%20x%20-%20300%3D0%20" alt="LaTeX: \displaystyle - 5 x^{2} - 80 x - 300=0 " data-equation-content=" \displaystyle - 5 x^{2} - 80 x - 300=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} + 16 x + 60) " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%5E%7B2%7D%20%2B%2016%20x%20%2B%2060%29%20" alt="LaTeX: \displaystyle -5(x^{2} + 16 x + 60) " data-equation-content=" \displaystyle -5(x^{2} + 16 x + 60) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle 60 " src="/equation_images/%20%5Cdisplaystyle%2060%20" alt="LaTeX: \displaystyle 60 " data-equation-content=" \displaystyle 60 " /> 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 6 " src="/equation_images/%20%5Cdisplaystyle%206%20" alt="LaTeX: \displaystyle 6 " data-equation-content=" \displaystyle 6 " /> and <img class="equation_image" title=" \displaystyle 10 " src="/equation_images/%20%5Cdisplaystyle%2010%20" alt="LaTeX: \displaystyle 10 " data-equation-content=" \displaystyle 10 " /> . This gives <img class="equation_image" title=" \displaystyle -5(x + 6)(x + 10)=0 " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%20%2B%206%29%28x%20%2B%2010%29%3D0%20" alt="LaTeX: \displaystyle -5(x + 6)(x + 10)=0 " data-equation-content=" \displaystyle -5(x + 6)(x + 10)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -6 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-6%20" alt="LaTeX: \displaystyle x = -6 " data-equation-content=" \displaystyle x = -6 " /> and <img class="equation_image" title=" \displaystyle x = -10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-10%20" alt="LaTeX: \displaystyle x = -10 " data-equation-content=" \displaystyle x = -10 " /> </p> </p>