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Algebra
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Solve. \(\displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 1\)

Squaring both sides gives \(\displaystyle x + 30=x + 2 \sqrt{x + 6} + 7\). Isolating the radical gives \(\displaystyle \frac{23}{2}=\sqrt{x + 6}\) Squaring again gives \(\displaystyle \frac{529}{4}=x + 6\). Solving for \(\displaystyle x\) gives \(\displaystyle x=\frac{505}{4}\). Checking the solution, \(\displaystyle x = \frac{505}{4}\), in the original equation gives \(\displaystyle \frac{25}{2} = \frac{25}{2}\) which is true so the solution checks.

Download \(\LaTeX\) 

\begin{question}Solve. $\sqrt{x + 30}=\sqrt{x + 6} + 1$
    \soln{10cm}{Squaring both sides gives $x + 30=x + 2 \sqrt{x + 6} + 7$. Isolating the radical gives $\frac{23}{2}=\sqrt{x + 6}$ Squaring again gives $\frac{529}{4}=x + 6$.  Solving for $x$ gives $x=\frac{505}{4}$. Checking the solution, $x = \frac{505}{4}$, in the original equation gives $\frac{25}{2} = \frac{25}{2}$ which is true so the solution checks.}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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    \soln{9cm}{The solution goes here.}

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HTML for Canvas 
<p> <p>Solve.  <img class="equation_image" title=" \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 1 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2030%7D%3D%5Csqrt%7Bx%20%2B%206%7D%20%2B%201%20" alt="LaTeX:  \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 1 " data-equation-content=" \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 1 " /> </p> </p>
HTML for Canvas
<p> <p>Squaring both sides gives  <img class="equation_image" title=" \displaystyle x + 30=x + 2 \sqrt{x + 6} + 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2030%3Dx%20%2B%202%20%5Csqrt%7Bx%20%2B%206%7D%20%2B%207%20" alt="LaTeX:  \displaystyle x + 30=x + 2 \sqrt{x + 6} + 7 " data-equation-content=" \displaystyle x + 30=x + 2 \sqrt{x + 6} + 7 " /> . Isolating the radical gives  <img class="equation_image" title=" \displaystyle \frac{23}{2}=\sqrt{x + 6} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B23%7D%7B2%7D%3D%5Csqrt%7Bx%20%2B%206%7D%20" alt="LaTeX:  \displaystyle \frac{23}{2}=\sqrt{x + 6} " data-equation-content=" \displaystyle \frac{23}{2}=\sqrt{x + 6} " />  Squaring again gives  <img class="equation_image" title=" \displaystyle \frac{529}{4}=x + 6 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B529%7D%7B4%7D%3Dx%20%2B%206%20" alt="LaTeX:  \displaystyle \frac{529}{4}=x + 6 " data-equation-content=" \displaystyle \frac{529}{4}=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=\frac{505}{4} " src="/equation_images/%20%5Cdisplaystyle%20x%3D%5Cfrac%7B505%7D%7B4%7D%20" alt="LaTeX:  \displaystyle x=\frac{505}{4} " data-equation-content=" \displaystyle x=\frac{505}{4} " /> . Checking the solution,  <img class="equation_image" title=" \displaystyle x = \frac{505}{4} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B505%7D%7B4%7D%20" alt="LaTeX:  \displaystyle x = \frac{505}{4} " data-equation-content=" \displaystyle x = \frac{505}{4} " /> , in the original equation gives  <img class="equation_image" title=" \displaystyle \frac{25}{2} = \frac{25}{2} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B25%7D%7B2%7D%20%3D%20%5Cfrac%7B25%7D%7B2%7D%20" alt="LaTeX:  \displaystyle \frac{25}{2} = \frac{25}{2} " data-equation-content=" \displaystyle \frac{25}{2} = \frac{25}{2} " />  which is true so the solution checks.</p> </p>