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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle - 15 x^{2} + 71 x - 70=0\)
Since the lead coefficient is negative factor out \(\displaystyle -1\). This is an ac method factoring. The factors of \(\displaystyle ac = 1050\) that add up to \(\displaystyle -71\) are \(\displaystyle -21\) and \(\displaystyle -50\). Separating gives \(\displaystyle (15 x^{2} - 21 x)+(70 - 50 x)=0\). This gives \(\displaystyle -1(3 x - 10)(5 x - 7)=0\). The solutions are \(\displaystyle x = \frac{10}{3}\) and \(\displaystyle x = \frac{7}{5}\)
\begin{question}Solve $- 15 x^{2} + 71 x - 70=0$
\soln{9cm}{Since the lead coefficient is negative factor out $-1$. This is an ac method factoring. The factors of $ac = 1050$ that add up to $-71$ are $-21$ and $-50$. Separating gives $(15 x^{2} - 21 x)+(70 - 50 x)=0$. This gives $-1(3 x - 10)(5 x - 7)=0$. The solutions are $x = \frac{10}{3}$ and $x = \frac{7}{5}$}
\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 - 15 x^{2} + 71 x - 70=0 " src="/equation_images/%20%5Cdisplaystyle%20-%2015%20x%5E%7B2%7D%20%2B%2071%20x%20-%2070%3D0%20" alt="LaTeX: \displaystyle - 15 x^{2} + 71 x - 70=0 " data-equation-content=" \displaystyle - 15 x^{2} + 71 x - 70=0 " /> </p> </p><p> <p>Since the lead coefficient is negative factor out <img class="equation_image" title=" \displaystyle -1 " src="/equation_images/%20%5Cdisplaystyle%20-1%20" alt="LaTeX: \displaystyle -1 " data-equation-content=" \displaystyle -1 " /> . This is an ac method factoring. The factors of <img class="equation_image" title=" \displaystyle ac = 1050 " src="/equation_images/%20%5Cdisplaystyle%20ac%20%3D%201050%20" alt="LaTeX: \displaystyle ac = 1050 " data-equation-content=" \displaystyle ac = 1050 " /> that add up to <img class="equation_image" title=" \displaystyle -71 " src="/equation_images/%20%5Cdisplaystyle%20-71%20" alt="LaTeX: \displaystyle -71 " data-equation-content=" \displaystyle -71 " /> are <img class="equation_image" title=" \displaystyle -21 " src="/equation_images/%20%5Cdisplaystyle%20-21%20" alt="LaTeX: \displaystyle -21 " data-equation-content=" \displaystyle -21 " /> and <img class="equation_image" title=" \displaystyle -50 " src="/equation_images/%20%5Cdisplaystyle%20-50%20" alt="LaTeX: \displaystyle -50 " data-equation-content=" \displaystyle -50 " /> . Separating gives <img class="equation_image" title=" \displaystyle (15 x^{2} - 21 x)+(70 - 50 x)=0 " src="/equation_images/%20%5Cdisplaystyle%20%2815%20x%5E%7B2%7D%20-%2021%20x%29%2B%2870%20-%2050%20x%29%3D0%20" alt="LaTeX: \displaystyle (15 x^{2} - 21 x)+(70 - 50 x)=0 " data-equation-content=" \displaystyle (15 x^{2} - 21 x)+(70 - 50 x)=0 " /> . This gives <img class="equation_image" title=" \displaystyle -1(3 x - 10)(5 x - 7)=0 " src="/equation_images/%20%5Cdisplaystyle%20-1%283%20x%20-%2010%29%285%20x%20-%207%29%3D0%20" alt="LaTeX: \displaystyle -1(3 x - 10)(5 x - 7)=0 " data-equation-content=" \displaystyle -1(3 x - 10)(5 x - 7)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = \frac{10}{3} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B10%7D%7B3%7D%20" alt="LaTeX: \displaystyle x = \frac{10}{3} " data-equation-content=" \displaystyle x = \frac{10}{3} " /> and <img class="equation_image" title=" \displaystyle x = \frac{7}{5} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B7%7D%7B5%7D%20" alt="LaTeX: \displaystyle x = \frac{7}{5} " data-equation-content=" \displaystyle x = \frac{7}{5} " /> </p> </p>