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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle x^{2} + 7 x + 10=0\)
Since \(\displaystyle a=1\) we need to find factors of \(\displaystyle 10\) that add up to \(\displaystyle 7\). The factors are \(\displaystyle 5\) and \(\displaystyle 2\). This gives \(\displaystyle (x + 5)(x + 2)=0\). The solutions are \(\displaystyle x = -5\) and \(\displaystyle x = -2\)
\begin{question}Solve $x^{2} + 7 x + 10=0$
\soln{9cm}{Since $a=1$ we need to find factors of $10$ that add up to $7$. The factors are $5$ and $2$. This gives $(x + 5)(x + 2)=0$. The solutions are $x = -5$ and $x = -2$}
\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 x^{2} + 7 x + 10=0 " src="/equation_images/%20%5Cdisplaystyle%20x%5E%7B2%7D%20%2B%207%20x%20%2B%2010%3D0%20" alt="LaTeX: \displaystyle x^{2} + 7 x + 10=0 " data-equation-content=" \displaystyle x^{2} + 7 x + 10=0 " /> </p> </p><p> <p>Since <img class="equation_image" title=" \displaystyle a=1 " src="/equation_images/%20%5Cdisplaystyle%20a%3D1%20" alt="LaTeX: \displaystyle a=1 " data-equation-content=" \displaystyle a=1 " /> we need to find factors of <img class="equation_image" title=" \displaystyle 10 " src="/equation_images/%20%5Cdisplaystyle%2010%20" alt="LaTeX: \displaystyle 10 " data-equation-content=" \displaystyle 10 " /> that add up to <img class="equation_image" title=" \displaystyle 7 " src="/equation_images/%20%5Cdisplaystyle%207%20" alt="LaTeX: \displaystyle 7 " data-equation-content=" \displaystyle 7 " /> . The factors are <img class="equation_image" title=" \displaystyle 5 " src="/equation_images/%20%5Cdisplaystyle%205%20" alt="LaTeX: \displaystyle 5 " data-equation-content=" \displaystyle 5 " /> and <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> . This gives <img class="equation_image" title=" \displaystyle (x + 5)(x + 2)=0 " src="/equation_images/%20%5Cdisplaystyle%20%28x%20%2B%205%29%28x%20%2B%202%29%3D0%20" alt="LaTeX: \displaystyle (x + 5)(x + 2)=0 " data-equation-content=" \displaystyle (x + 5)(x + 2)=0 " /> . The solutions are <img class="equation_image" title=" \displaystyle x = -5 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-5%20" alt="LaTeX: \displaystyle x = -5 " data-equation-content=" \displaystyle x = -5 " /> and <img class="equation_image" title=" \displaystyle x = -2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-2%20" alt="LaTeX: \displaystyle x = -2 " data-equation-content=" \displaystyle x = -2 " /> </p> </p>