Solve. $LaTeX: \displaystyle \sqrt{x + 18}=\sqrt{x - 8} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 18=x + 4 \sqrt{x - 8} - 4$ . Isolating the radical gives $LaTeX: \displaystyle \frac{11}{2}=\sqrt{x - 8}$ Squaring again gives $LaTeX: \displaystyle \frac{121}{4}=x - 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{153}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{153}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{15}{2} = \frac{15}{2}$ which is true so the solution checks.