Solve. $LaTeX: \displaystyle \sqrt{x + 20}=\sqrt{x - 2} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 20=x + 4 \sqrt{x - 2} + 2$ . Isolating the radical gives $LaTeX: \displaystyle \frac{9}{2}=\sqrt{x - 2}$ Squaring again gives $LaTeX: \displaystyle \frac{81}{4}=x - 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{89}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{89}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{13}{2} = \frac{13}{2}$ which is true so the solution checks.