Solve. $LaTeX: \displaystyle \sqrt{x + 20}=\sqrt{x - 2} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 20=x + 6 \sqrt{x - 2} + 7$ . Isolating the radical gives $LaTeX: \displaystyle \frac{13}{6}=\sqrt{x - 2}$ Squaring again gives $LaTeX: \displaystyle \frac{169}{36}=x - 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{241}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{241}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{31}{6} = \frac{31}{6}$ which is true so the solution checks.