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Algebra
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Solve. \(\displaystyle \sqrt{x + 18}=\sqrt{x - 2} + 3\)

Squaring both sides gives \(\displaystyle x + 18=x + 6 \sqrt{x - 2} + 7\). Isolating the radical gives \(\displaystyle \frac{11}{6}=\sqrt{x - 2}\) Squaring again gives \(\displaystyle \frac{121}{36}=x - 2\). Solving for \(\displaystyle x\) gives \(\displaystyle x=\frac{193}{36}\). Checking the solution, \(\displaystyle x = \frac{193}{36}\), in the original equation gives \(\displaystyle \frac{29}{6} = \frac{29}{6}\) which is true so the solution checks.

Download \(\LaTeX\) 

\begin{question}Solve. $\sqrt{x + 18}=\sqrt{x - 2} + 3$
    \soln{10cm}{Squaring both sides gives $x + 18=x + 6 \sqrt{x - 2} + 7$. Isolating the radical gives $\frac{11}{6}=\sqrt{x - 2}$ Squaring again gives $\frac{121}{36}=x - 2$.  Solving for $x$ gives $x=\frac{193}{36}$. Checking the solution, $x = \frac{193}{36}$, in the original equation gives $\frac{29}{6} = \frac{29}{6}$ which is true so the solution checks.}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Solve.  <img class="equation_image" title=" \displaystyle \sqrt{x + 18}=\sqrt{x - 2} + 3 " src="/equation_images/%20%5Cdisplaystyle%20%5Csqrt%7Bx%20%2B%2018%7D%3D%5Csqrt%7Bx%20-%202%7D%20%2B%203%20" alt="LaTeX:  \displaystyle \sqrt{x + 18}=\sqrt{x - 2} + 3 " data-equation-content=" \displaystyle \sqrt{x + 18}=\sqrt{x - 2} + 3 " /> </p> </p>
HTML for Canvas
<p> <p>Squaring both sides gives  <img class="equation_image" title=" \displaystyle x + 18=x + 6 \sqrt{x - 2} + 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%2B%2018%3Dx%20%2B%206%20%5Csqrt%7Bx%20-%202%7D%20%2B%207%20" alt="LaTeX:  \displaystyle x + 18=x + 6 \sqrt{x - 2} + 7 " data-equation-content=" \displaystyle x + 18=x + 6 \sqrt{x - 2} + 7 " /> . Isolating the radical gives  <img class="equation_image" title=" \displaystyle \frac{11}{6}=\sqrt{x - 2} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B11%7D%7B6%7D%3D%5Csqrt%7Bx%20-%202%7D%20" alt="LaTeX:  \displaystyle \frac{11}{6}=\sqrt{x - 2} " data-equation-content=" \displaystyle \frac{11}{6}=\sqrt{x - 2} " />  Squaring again gives  <img class="equation_image" title=" \displaystyle \frac{121}{36}=x - 2 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B121%7D%7B36%7D%3Dx%20-%202%20" alt="LaTeX:  \displaystyle \frac{121}{36}=x - 2 " data-equation-content=" \displaystyle \frac{121}{36}=x - 2 " /> .  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{193}{36} " src="/equation_images/%20%5Cdisplaystyle%20x%3D%5Cfrac%7B193%7D%7B36%7D%20" alt="LaTeX:  \displaystyle x=\frac{193}{36} " data-equation-content=" \displaystyle x=\frac{193}{36} " /> . Checking the solution,  <img class="equation_image" title=" \displaystyle x = \frac{193}{36} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B193%7D%7B36%7D%20" alt="LaTeX:  \displaystyle x = \frac{193}{36} " data-equation-content=" \displaystyle x = \frac{193}{36} " /> , in the original equation gives  <img class="equation_image" title=" \displaystyle \frac{29}{6} = \frac{29}{6} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B29%7D%7B6%7D%20%3D%20%5Cfrac%7B29%7D%7B6%7D%20" alt="LaTeX:  \displaystyle \frac{29}{6} = \frac{29}{6} " data-equation-content=" \displaystyle \frac{29}{6} = \frac{29}{6} " />  which is true so the solution checks.</p> </p>