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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle 6 x^{2} - 5 x - 25=0\)
This is an ac method factoring. The factors of \(\displaystyle ac = -150\) that add up to \(\displaystyle -5\) are \(\displaystyle -15\) and \(\displaystyle 10\). Separating gives \(\displaystyle (6 x^{2} - 15 x)+(10 x - 25)=0\). This gives \(\displaystyle (3 x + 5)(2 x - 5)=0\). The solutions are \(\displaystyle x = - \frac{5}{3}\) and \(\displaystyle x = \frac{5}{2}\)
\begin{question}Solve $6 x^{2} - 5 x - 25=0$
\soln{9cm}{This is an ac method factoring. The factors of $ac = -150$ that add up to $-5$ are $-15$ and $10$. Separating gives $(6 x^{2} - 15 x)+(10 x - 25)=0$. This gives $(3 x + 5)(2 x - 5)=0$. The solutions are $x = - \frac{5}{3}$ and $x = \frac{5}{2}$}
\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 6 x^{2} - 5 x - 25=0 " src="/equation_images/%20%5Cdisplaystyle%206%20x%5E%7B2%7D%20-%205%20x%20-%2025%3D0%20" alt="LaTeX: \displaystyle 6 x^{2} - 5 x - 25=0 " data-equation-content=" \displaystyle 6 x^{2} - 5 x - 25=0 " /> </p> </p><p> <p>This is an ac method factoring. The factors of <img class="equation_image" title=" \displaystyle ac = -150 " src="/equation_images/%20%5Cdisplaystyle%20ac%20%3D%20-150%20" alt="LaTeX: \displaystyle ac = -150 " data-equation-content=" \displaystyle ac = -150 " /> that add up to <img class="equation_image" title=" \displaystyle -5 " src="/equation_images/%20%5Cdisplaystyle%20-5%20" alt="LaTeX: \displaystyle -5 " data-equation-content=" \displaystyle -5 " /> are <img class="equation_image" title=" \displaystyle -15 " src="/equation_images/%20%5Cdisplaystyle%20-15%20" alt="LaTeX: \displaystyle -15 " data-equation-content=" \displaystyle -15 " /> and <img class="equation_image" title=" \displaystyle 10 " src="/equation_images/%20%5Cdisplaystyle%2010%20" alt="LaTeX: \displaystyle 10 " data-equation-content=" \displaystyle 10 " /> . Separating gives <img class="equation_image" title=" \displaystyle (6 x^{2} - 15 x)+(10 x - 25)=0 " src="/equation_images/%20%5Cdisplaystyle%20%286%20x%5E%7B2%7D%20-%2015%20x%29%2B%2810%20x%20-%2025%29%3D0%20" alt="LaTeX: \displaystyle (6 x^{2} - 15 x)+(10 x - 25)=0 " data-equation-content=" \displaystyle (6 x^{2} - 15 x)+(10 x - 25)=0 " /> . This gives <img class="equation_image" title=" \displaystyle (3 x + 5)(2 x - 5)=0 " src="/equation_images/%20%5Cdisplaystyle%20%283%20x%20%2B%205%29%282%20x%20-%205%29%3D0%20" alt="LaTeX: \displaystyle (3 x + 5)(2 x - 5)=0 " data-equation-content=" \displaystyle (3 x + 5)(2 x - 5)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = - \frac{5}{3} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20%5Cfrac%7B5%7D%7B3%7D%20" alt="LaTeX: \displaystyle x = - \frac{5}{3} " data-equation-content=" \displaystyle x = - \frac{5}{3} " /> and <img class="equation_image" title=" \displaystyle x = \frac{5}{2} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20" alt="LaTeX: \displaystyle x = \frac{5}{2} " data-equation-content=" \displaystyle x = \frac{5}{2} " /> </p> </p>