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

Squaring both sides gives $LaTeX: \displaystyle x + 20=x - 6 \sqrt{x + 2} + 11$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{3}{2}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{4}=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{1}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{1}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{9}{2} = - \frac{3}{2}$ which is false so it is an extraneous solution and there is no solution.