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Questions: Algebra BusinessCalculus
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Solve. \(\displaystyle \sqrt{x + 32}=\sqrt{x - 4} - 2\)
Squaring both sides gives \(\displaystyle x + 32=x - 4 \sqrt{x - 4}\). Isolating the radical gives \(\displaystyle -8=\sqrt{x - 4}\) Squaring again gives \(\displaystyle 64=x - 4\). Solving for \(\displaystyle x\) gives \(\displaystyle x=68\). Checking the solution, \(\displaystyle x = 68\), in the original equation gives \(\displaystyle 10 = 6\) which is false so it is an extraneous solution and there is no solution.
\begin{question}Solve. $\sqrt{x + 32}=\sqrt{x - 4} - 2$
\soln{10cm}{Squaring both sides gives $x + 32=x - 4 \sqrt{x - 4}$. Isolating the radical gives $-8=\sqrt{x - 4}$ Squaring again gives $64=x - 4$. Solving for $x$ gives $x=68$. Checking the solution, $x = 68$, in the original equation gives $10 = 6$ which is false so it is an extraneous solution and there is no solution.}
\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 + 32}=\sqrt{x - 4} - 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2032%7D%3D%5Csqrt%7Bx%20-%204%7D%20-%202%20" alt="LaTeX: \displaystyle \sqrt{x + 32}=\sqrt{x - 4} - 2 " data-equation-content=" \displaystyle \sqrt{x + 32}=\sqrt{x - 4} - 2 " /> </p> </p><p> <p>Squaring both sides gives <img class="equation_image" title=" \displaystyle x + 32=x - 4 \sqrt{x - 4} " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2032%3Dx%20-%204%20%5Csqrt%7Bx%20-%204%7D%20" alt="LaTeX: \displaystyle x + 32=x - 4 \sqrt{x - 4} " data-equation-content=" \displaystyle x + 32=x - 4 \sqrt{x - 4} " /> . Isolating the radical gives <img class="equation_image" title=" \displaystyle -8=\sqrt{x - 4} " src="/equation_images/%20%5Cdisplaystyle%20-8%3D%5Csqrt%7Bx%20-%204%7D%20" alt="LaTeX: \displaystyle -8=\sqrt{x - 4} " data-equation-content=" \displaystyle -8=\sqrt{x - 4} " /> Squaring again gives <img class="equation_image" title=" \displaystyle 64=x - 4 " src="/equation_images/%20%5Cdisplaystyle%2064%3Dx%20-%204%20" alt="LaTeX: \displaystyle 64=x - 4 " data-equation-content=" \displaystyle 64=x - 4 " /> . 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=68 " src="/equation_images/%20%5Cdisplaystyle%20x%3D68%20" alt="LaTeX: \displaystyle x=68 " data-equation-content=" \displaystyle x=68 " /> . Checking the solution, <img class="equation_image" title=" \displaystyle x = 68 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2068%20" alt="LaTeX: \displaystyle x = 68 " data-equation-content=" \displaystyle x = 68 " /> , in the original equation gives <img class="equation_image" title=" \displaystyle 10 = 6 " src="/equation_images/%20%5Cdisplaystyle%2010%20%3D%206%20" alt="LaTeX: \displaystyle 10 = 6 " data-equation-content=" \displaystyle 10 = 6 " /> which is false so it is an extraneous solution and there is no solution.</p> </p>