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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 20 x^{2} - 67 x + 56=0\)
This is an ac method factoring. The factors of \(\displaystyle ac = 1120\) that add up to \(\displaystyle -67\) are \(\displaystyle -35\) and \(\displaystyle -32\). Separating gives \(\displaystyle (20 x^{2} - 35 x)+(56 - 32 x)=0\). This gives \(\displaystyle (5 x - 8)(4 x - 7)=0\). The solutions are \(\displaystyle x = \frac{8}{5}\) and \(\displaystyle x = \frac{7}{4}\)
\begin{question}Solve $20 x^{2} - 67 x + 56=0$
\soln{9cm}{This is an ac method factoring. The factors of $ac = 1120$ that add up to $-67$ are $-35$ and $-32$. Separating gives $(20 x^{2} - 35 x)+(56 - 32 x)=0$. This gives $(5 x - 8)(4 x - 7)=0$. The solutions are $x = \frac{8}{5}$ and $x = \frac{7}{4}$}
\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 20 x^{2} - 67 x + 56=0 " src="/equation_images/%20%5Cdisplaystyle%2020%20x%5E%7B2%7D%20-%2067%20x%20%2B%2056%3D0%20" alt="LaTeX: \displaystyle 20 x^{2} - 67 x + 56=0 " data-equation-content=" \displaystyle 20 x^{2} - 67 x + 56=0 " /> </p> </p><p> <p>This is an ac method factoring. The factors of <img class="equation_image" title=" \displaystyle ac = 1120 " src="/equation_images/%20%5Cdisplaystyle%20ac%20%3D%201120%20" alt="LaTeX: \displaystyle ac = 1120 " data-equation-content=" \displaystyle ac = 1120 " /> that add up to <img class="equation_image" title=" \displaystyle -67 " src="/equation_images/%20%5Cdisplaystyle%20-67%20" alt="LaTeX: \displaystyle -67 " data-equation-content=" \displaystyle -67 " /> are <img class="equation_image" title=" \displaystyle -35 " src="/equation_images/%20%5Cdisplaystyle%20-35%20" alt="LaTeX: \displaystyle -35 " data-equation-content=" \displaystyle -35 " /> and <img class="equation_image" title=" \displaystyle -32 " src="/equation_images/%20%5Cdisplaystyle%20-32%20" alt="LaTeX: \displaystyle -32 " data-equation-content=" \displaystyle -32 " /> . Separating gives <img class="equation_image" title=" \displaystyle (20 x^{2} - 35 x)+(56 - 32 x)=0 " src="/equation_images/%20%5Cdisplaystyle%20%2820%20x%5E%7B2%7D%20-%2035%20x%29%2B%2856%20-%2032%20x%29%3D0%20" alt="LaTeX: \displaystyle (20 x^{2} - 35 x)+(56 - 32 x)=0 " data-equation-content=" \displaystyle (20 x^{2} - 35 x)+(56 - 32 x)=0 " /> . This gives <img class="equation_image" title=" \displaystyle (5 x - 8)(4 x - 7)=0 " src="/equation_images/%20%5Cdisplaystyle%20%285%20x%20-%208%29%284%20x%20-%207%29%3D0%20" alt="LaTeX: \displaystyle (5 x - 8)(4 x - 7)=0 " data-equation-content=" \displaystyle (5 x - 8)(4 x - 7)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = \frac{8}{5} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B8%7D%7B5%7D%20" alt="LaTeX: \displaystyle x = \frac{8}{5} " data-equation-content=" \displaystyle x = \frac{8}{5} " /> and <img class="equation_image" title=" \displaystyle x = \frac{7}{4} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B7%7D%7B4%7D%20" alt="LaTeX: \displaystyle x = \frac{7}{4} " data-equation-content=" \displaystyle x = \frac{7}{4} " /> </p> </p>