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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 2 x^{2} + 4 x + 6=0\)
Since the GCF is \(\displaystyle -2\) we need we factor out the GCF to get \(\displaystyle -2(x^{2} - 2 x - 3)\). This is now a pq method factoring. The factors of \(\displaystyle -3\) that add up to \(\displaystyle -2\) are \(\displaystyle 1\) and \(\displaystyle -3\). This gives \(\displaystyle -2(x + 1)(x - 3)=0\). The solutions are \(\displaystyle x = -1\) and \(\displaystyle x = 3\)
\begin{question}Solve $- 2 x^{2} + 4 x + 6=0$
\soln{9cm}{Since the GCF is $-2$ we need we factor out the GCF to get $-2(x^{2} - 2 x - 3)$. This is now a pq method factoring. The factors of $-3$ that add up to $-2$ are $1$ and $-3$. This gives $-2(x + 1)(x - 3)=0$. The solutions are $x = -1$ and $x = 3$}
\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} + 4 x + 6=0 " src="/equation_images/%20%5Cdisplaystyle%20-%202%20x%5E%7B2%7D%20%2B%204%20x%20%2B%206%3D0%20" alt="LaTeX: \displaystyle - 2 x^{2} + 4 x + 6=0 " data-equation-content=" \displaystyle - 2 x^{2} + 4 x + 6=0 " /> </p> </p><p> <p>Since the GCF is <img class="equation_image" title=" \displaystyle -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%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} - 2 x - 3) " src="/equation_images/%20%5Cdisplaystyle%20-2%28x%5E%7B2%7D%20-%202%20x%20-%203%29%20" alt="LaTeX: \displaystyle -2(x^{2} - 2 x - 3) " data-equation-content=" \displaystyle -2(x^{2} - 2 x - 3) " /> . This is now a pq method factoring. The factors of <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> that add up to <img class="equation_image" title=" \displaystyle -2 " src="/equation_images/%20%5Cdisplaystyle%20-2%20" alt="LaTeX: \displaystyle -2 " data-equation-content=" \displaystyle -2 " /> are <img class="equation_image" title=" \displaystyle 1 " src="/equation_images/%20%5Cdisplaystyle%201%20" alt="LaTeX: \displaystyle 1 " data-equation-content=" \displaystyle 1 " /> and <img class="equation_image" title=" \displaystyle -3 " src="/equation_images/%20%5Cdisplaystyle%20-3%20" alt="LaTeX: \displaystyle -3 " data-equation-content=" \displaystyle -3 " /> . This gives <img class="equation_image" title=" \displaystyle -2(x + 1)(x - 3)=0 " src="/equation_images/%20%5Cdisplaystyle%20-2%28x%20%2B%201%29%28x%20-%203%29%3D0%20" alt="LaTeX: \displaystyle -2(x + 1)(x - 3)=0 " data-equation-content=" \displaystyle -2(x + 1)(x - 3)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -1 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-1%20" alt="LaTeX: \displaystyle x = -1 " data-equation-content=" \displaystyle x = -1 " /> and <img class="equation_image" title=" \displaystyle x = 3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%203%20" alt="LaTeX: \displaystyle x = 3 " data-equation-content=" \displaystyle x = 3 " /> </p> </p>