Solve. $LaTeX: \displaystyle \sqrt{x + 20}=\sqrt{x + 6} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 20=x - 4 \sqrt{x + 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{5}{2}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{25}{4}=x + 6$ . 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 $LaTeX: \displaystyle \frac{9}{2} = \frac{1}{2}$ which is false so it is an extraneous solution and there is no solution.