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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 5 x^{2} + 15 x + 350=0\)
Since the GCF is \(\displaystyle -5\) we need we factor out the GCF to get \(\displaystyle -5(x^{2} - 3 x - 70)\). This is now a pq method factoring. The factors of \(\displaystyle -70\) that add up to \(\displaystyle -3\) are \(\displaystyle -10\) and \(\displaystyle 7\). This gives \(\displaystyle -5(x - 10)(x + 7)=0\). The solutions are \(\displaystyle x = 10\) and \(\displaystyle x = -7\)
\begin{question}Solve $- 5 x^{2} + 15 x + 350=0$
\soln{9cm}{Since the GCF is $-5$ we need we factor out the GCF to get $-5(x^{2} - 3 x - 70)$. This is now a pq method factoring. The factors of $-70$ that add up to $-3$ are $-10$ and $7$. This gives $-5(x - 10)(x + 7)=0$. The solutions are $x = 10$ 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 - 5 x^{2} + 15 x + 350=0 " src="/equation_images/%20%5Cdisplaystyle%20-%205%20x%5E%7B2%7D%20%2B%2015%20x%20%2B%20350%3D0%20" alt="LaTeX: \displaystyle - 5 x^{2} + 15 x + 350=0 " data-equation-content=" \displaystyle - 5 x^{2} + 15 x + 350=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} - 3 x - 70) " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%5E%7B2%7D%20-%203%20x%20-%2070%29%20" alt="LaTeX: \displaystyle -5(x^{2} - 3 x - 70) " data-equation-content=" \displaystyle -5(x^{2} - 3 x - 70) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -70 " src="/equation_images/%20%5Cdisplaystyle%20-70%20" alt="LaTeX: \displaystyle -70 " data-equation-content=" \displaystyle -70 " /> that add up to <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> are <img class="equation_image" title=" \displaystyle -10 " src="/equation_images/%20%5Cdisplaystyle%20-10%20" alt="LaTeX: \displaystyle -10 " data-equation-content=" \displaystyle -10 " /> 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 -5(x - 10)(x + 7)=0 " src="/equation_images/%20%5Cdisplaystyle%20-5%28x%20-%2010%29%28x%20%2B%207%29%3D0%20" alt="LaTeX: \displaystyle -5(x - 10)(x + 7)=0 " data-equation-content=" \displaystyle -5(x - 10)(x + 7)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = 10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2010%20" alt="LaTeX: \displaystyle x = 10 " data-equation-content=" \displaystyle x = 10 " /> 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>