Solve. $LaTeX: \displaystyle \sqrt{x + 20}=\sqrt{x - 8} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 20=x - 4 \sqrt{x - 8} - 4$ . Isolating the radical gives $LaTeX: \displaystyle -6=\sqrt{x - 8}$ Squaring again gives $LaTeX: \displaystyle 36=x - 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=44$ . Checking the solution, $LaTeX: \displaystyle x = 44$ , in the original equation gives $LaTeX: \displaystyle 8 = 4$ which is false so it is an extraneous solution and there is no solution.