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

Squaring both sides gives $LaTeX: \displaystyle x + 20=x - 4 \sqrt{x + 8} + 12$ . Isolating the radical gives $LaTeX: \displaystyle -2=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle 4=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=-4$ . Checking the solution, $LaTeX: \displaystyle x = -4$ , in the original equation gives $LaTeX: \displaystyle 4 = 0$ which is false so it is an extraneous solution and there is no solution.