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Questions: Algebra BusinessCalculus
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Solve. \(\displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 2\)
Squaring both sides gives \(\displaystyle x + 30=x + 4 \sqrt{x + 6} + 10\). Isolating the radical gives \(\displaystyle 5=\sqrt{x + 6}\) Squaring again gives \(\displaystyle 25=x + 6\). Solving for \(\displaystyle x\) gives \(\displaystyle x=19\). Checking the solution, \(\displaystyle x = 19\), in the original equation gives \(\displaystyle 7 = 7\) which is true so the solution checks.
\begin{question}Solve. $\sqrt{x + 30}=\sqrt{x + 6} + 2$
\soln{10cm}{Squaring both sides gives $x + 30=x + 4 \sqrt{x + 6} + 10$. Isolating the radical gives $5=\sqrt{x + 6}$ Squaring again gives $25=x + 6$. Solving for $x$ gives $x=19$. Checking the solution, $x = 19$, in the original equation gives $7 = 7$ 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 + 30}=\sqrt{x + 6} + 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2030%7D%3D%5Csqrt%7Bx%20%2B%206%7D%20%2B%202%20" alt="LaTeX: \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 2 " data-equation-content=" \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 2 " /> </p> </p><p> <p>Squaring both sides gives <img class="equation_image" title=" \displaystyle x + 30=x + 4 \sqrt{x + 6} + 10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2030%3Dx%20%2B%204%20%5Csqrt%7Bx%20%2B%206%7D%20%2B%2010%20" alt="LaTeX: \displaystyle x + 30=x + 4 \sqrt{x + 6} + 10 " data-equation-content=" \displaystyle x + 30=x + 4 \sqrt{x + 6} + 10 " /> . Isolating the radical gives <img class="equation_image" title=" \displaystyle 5=\sqrt{x + 6} " src="/equation_images/%20%5Cdisplaystyle%205%3D%5Csqrt%7Bx%20%2B%206%7D%20" alt="LaTeX: \displaystyle 5=\sqrt{x + 6} " data-equation-content=" \displaystyle 5=\sqrt{x + 6} " /> Squaring again gives <img class="equation_image" title=" \displaystyle 25=x + 6 " src="/equation_images/%20%5Cdisplaystyle%2025%3Dx%20%2B%206%20" alt="LaTeX: \displaystyle 25=x + 6 " data-equation-content=" \displaystyle 25=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=19 " src="/equation_images/%20%5Cdisplaystyle%20x%3D19%20" alt="LaTeX: \displaystyle x=19 " data-equation-content=" \displaystyle x=19 " /> . Checking the solution, <img class="equation_image" title=" \displaystyle x = 19 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2019%20" alt="LaTeX: \displaystyle x = 19 " data-equation-content=" \displaystyle x = 19 " /> , in the original equation gives <img class="equation_image" title=" \displaystyle 7 = 7 " src="/equation_images/%20%5Cdisplaystyle%207%20%3D%207%20" alt="LaTeX: \displaystyle 7 = 7 " data-equation-content=" \displaystyle 7 = 7 " /> which is true so the solution checks.</p> </p>