Solve. $LaTeX: \displaystyle \sqrt{x + 24}=\sqrt{x - 8} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 24=x - 4 \sqrt{x - 8} - 4$ . Isolating the radical gives $LaTeX: \displaystyle -7=\sqrt{x - 8}$ Squaring again gives $LaTeX: \displaystyle 49=x - 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=57$ . Checking the solution, $LaTeX: \displaystyle x = 57$ , in the original equation gives $LaTeX: \displaystyle 9 = 5$ which is false so it is an extraneous solution and there is no solution.