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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 3 x^{2} - 57 x - 270=0\)
Since the GCF is \(\displaystyle -3\) we need we factor out the GCF to get \(\displaystyle -3(x^{2} + 19 x + 90)\). This is now a pq method factoring. The factors of \(\displaystyle 90\) that add up to \(\displaystyle 19\) are \(\displaystyle 10\) and \(\displaystyle 9\). This gives \(\displaystyle -3(x + 10)(x + 9)=0\). The solutions are \(\displaystyle x = -10\) and \(\displaystyle x = -9\)
\begin{question}Solve $- 3 x^{2} - 57 x - 270=0$
\soln{9cm}{Since the GCF is $-3$ we need we factor out the GCF to get $-3(x^{2} + 19 x + 90)$. This is now a pq method factoring. The factors of $90$ that add up to $19$ are $10$ and $9$. This gives $-3(x + 10)(x + 9)=0$. The solutions are $x = -10$ 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 - 3 x^{2} - 57 x - 270=0 " src="/equation_images/%20%5Cdisplaystyle%20-%203%20x%5E%7B2%7D%20-%2057%20x%20-%20270%3D0%20" alt="LaTeX: \displaystyle - 3 x^{2} - 57 x - 270=0 " data-equation-content=" \displaystyle - 3 x^{2} - 57 x - 270=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> we need we factor out the GCF to get <img class="equation_image" title=" \displaystyle -3(x^{2} + 19 x + 90) " src="/equation_images/%20%5Cdisplaystyle%20-3%28x%5E%7B2%7D%20%2B%2019%20x%20%2B%2090%29%20" alt="LaTeX: \displaystyle -3(x^{2} + 19 x + 90) " data-equation-content=" \displaystyle -3(x^{2} + 19 x + 90) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle 90 " src="/equation_images/%20%5Cdisplaystyle%2090%20" alt="LaTeX: \displaystyle 90 " data-equation-content=" \displaystyle 90 " /> that add up to <img class="equation_image" title=" \displaystyle 19 " src="/equation_images/%20%5Cdisplaystyle%2019%20" alt="LaTeX: \displaystyle 19 " data-equation-content=" \displaystyle 19 " /> are <img class="equation_image" title=" \displaystyle 10 " src="/equation_images/%20%5Cdisplaystyle%2010%20" alt="LaTeX: \displaystyle 10 " data-equation-content=" \displaystyle 10 " /> and <img class="equation_image" title=" \displaystyle 9 " src="/equation_images/%20%5Cdisplaystyle%209%20" alt="LaTeX: \displaystyle 9 " data-equation-content=" \displaystyle 9 " /> . This gives <img class="equation_image" title=" \displaystyle -3(x + 10)(x + 9)=0 " src="/equation_images/%20%5Cdisplaystyle%20-3%28x%20%2B%2010%29%28x%20%2B%209%29%3D0%20" alt="LaTeX: \displaystyle -3(x + 10)(x + 9)=0 " data-equation-content=" \displaystyle -3(x + 10)(x + 9)=0 " /> . The solutions are <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 " /> and <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 " /> </p> </p>