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Questions: Algebra BusinessCalculus
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Solve. \(\displaystyle \sqrt{x + 26}=\sqrt{x - 6} + 2\)
Squaring both sides gives \(\displaystyle x + 26=x + 4 \sqrt{x - 6} - 2\). Isolating the radical gives \(\displaystyle 7=\sqrt{x - 6}\) Squaring again gives \(\displaystyle 49=x - 6\). Solving for \(\displaystyle x\) gives \(\displaystyle x=55\). Checking the solution, \(\displaystyle x = 55\), in the original equation gives \(\displaystyle 9 = 9\) which is true so the solution checks.
\begin{question}Solve. $\sqrt{x + 26}=\sqrt{x - 6} + 2$
\soln{10cm}{Squaring both sides gives $x + 26=x + 4 \sqrt{x - 6} - 2$. Isolating the radical gives $7=\sqrt{x - 6}$ Squaring again gives $49=x - 6$. Solving for $x$ gives $x=55$. Checking the solution, $x = 55$, in the original equation gives $9 = 9$ which is true so the solution checks.}
\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 \sqrt{x + 26}=\sqrt{x - 6} + 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2026%7D%3D%5Csqrt%7Bx%20-%206%7D%20%2B%202%20" alt="LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x - 6} + 2 " data-equation-content=" \displaystyle \sqrt{x + 26}=\sqrt{x - 6} + 2 " /> </p> </p><p> <p>Squaring both sides gives <img class="equation_image" title=" \displaystyle x + 26=x + 4 \sqrt{x - 6} - 2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2026%3Dx%20%2B%204%20%5Csqrt%7Bx%20-%206%7D%20-%202%20" alt="LaTeX: \displaystyle x + 26=x + 4 \sqrt{x - 6} - 2 " data-equation-content=" \displaystyle x + 26=x + 4 \sqrt{x - 6} - 2 " /> . Isolating the radical gives <img class="equation_image" title=" \displaystyle 7=\sqrt{x - 6} " src="/equation_images/%20%5Cdisplaystyle%207%3D%5Csqrt%7Bx%20-%206%7D%20" alt="LaTeX: \displaystyle 7=\sqrt{x - 6} " data-equation-content=" \displaystyle 7=\sqrt{x - 6} " /> Squaring again gives <img class="equation_image" title=" \displaystyle 49=x - 6 " src="/equation_images/%20%5Cdisplaystyle%2049%3Dx%20-%206%20" alt="LaTeX: \displaystyle 49=x - 6 " data-equation-content=" \displaystyle 49=x - 6 " /> . Solving for <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x=55 " src="/equation_images/%20%5Cdisplaystyle%20x%3D55%20" alt="LaTeX: \displaystyle x=55 " data-equation-content=" \displaystyle x=55 " /> . Checking the solution, <img class="equation_image" title=" \displaystyle x = 55 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2055%20" alt="LaTeX: \displaystyle x = 55 " data-equation-content=" \displaystyle x = 55 " /> , in the original equation gives <img class="equation_image" title=" \displaystyle 9 = 9 " src="/equation_images/%20%5Cdisplaystyle%209%20%3D%209%20" alt="LaTeX: \displaystyle 9 = 9 " data-equation-content=" \displaystyle 9 = 9 " /> which is true so the solution checks.</p> </p>