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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 8 x^{2} + 30 x + 7=0\)
This is an ac method factoring. The factors of \(\displaystyle ac = 56\) that add up to \(\displaystyle 30\) are \(\displaystyle 2\) and \(\displaystyle 28\). Separating gives \(\displaystyle (8 x^{2} + 2 x)+(28 x + 7)=0\). This gives \(\displaystyle (2 x + 7)(4 x + 1)=0\). The solutions are \(\displaystyle x = - \frac{7}{2}\) and \(\displaystyle x = - \frac{1}{4}\)
\begin{question}Solve $8 x^{2} + 30 x + 7=0$
\soln{9cm}{This is an ac method factoring. The factors of $ac = 56$ that add up to $30$ are $2$ and $28$. Separating gives $(8 x^{2} + 2 x)+(28 x + 7)=0$. This gives $(2 x + 7)(4 x + 1)=0$. The solutions are $x = - \frac{7}{2}$ and $x = - \frac{1}{4}$}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle 8 x^{2} + 30 x + 7=0 " src="/equation_images/%20%5Cdisplaystyle%208%20x%5E%7B2%7D%20%2B%2030%20x%20%2B%207%3D0%20" alt="LaTeX: \displaystyle 8 x^{2} + 30 x + 7=0 " data-equation-content=" \displaystyle 8 x^{2} + 30 x + 7=0 " /> </p> </p><p> <p>This is an ac method factoring. The factors of <img class="equation_image" title=" \displaystyle ac = 56 " src="/equation_images/%20%5Cdisplaystyle%20ac%20%3D%2056%20" alt="LaTeX: \displaystyle ac = 56 " data-equation-content=" \displaystyle ac = 56 " /> that add up to <img class="equation_image" title=" \displaystyle 30 " src="/equation_images/%20%5Cdisplaystyle%2030%20" alt="LaTeX: \displaystyle 30 " data-equation-content=" \displaystyle 30 " /> are <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> and <img class="equation_image" title=" \displaystyle 28 " src="/equation_images/%20%5Cdisplaystyle%2028%20" alt="LaTeX: \displaystyle 28 " data-equation-content=" \displaystyle 28 " /> . Separating gives <img class="equation_image" title=" \displaystyle (8 x^{2} + 2 x)+(28 x + 7)=0 " src="/equation_images/%20%5Cdisplaystyle%20%288%20x%5E%7B2%7D%20%2B%202%20x%29%2B%2828%20x%20%2B%207%29%3D0%20" alt="LaTeX: \displaystyle (8 x^{2} + 2 x)+(28 x + 7)=0 " data-equation-content=" \displaystyle (8 x^{2} + 2 x)+(28 x + 7)=0 " /> . This gives <img class="equation_image" title=" \displaystyle (2 x + 7)(4 x + 1)=0 " src="/equation_images/%20%5Cdisplaystyle%20%282%20x%20%2B%207%29%284%20x%20%2B%201%29%3D0%20" alt="LaTeX: \displaystyle (2 x + 7)(4 x + 1)=0 " data-equation-content=" \displaystyle (2 x + 7)(4 x + 1)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = - \frac{7}{2} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20%5Cfrac%7B7%7D%7B2%7D%20" alt="LaTeX: \displaystyle x = - \frac{7}{2} " data-equation-content=" \displaystyle x = - \frac{7}{2} " /> and <img class="equation_image" title=" \displaystyle x = - \frac{1}{4} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20%5Cfrac%7B1%7D%7B4%7D%20" alt="LaTeX: \displaystyle x = - \frac{1}{4} " data-equation-content=" \displaystyle x = - \frac{1}{4} " /> </p> </p>