Solve. $LaTeX: \displaystyle \sqrt{x + 32}=\sqrt{x - 4} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 32=x - 4 \sqrt{x - 4}$ . Isolating the radical gives $LaTeX: \displaystyle -8=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle 64=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=68$ . Checking the solution, $LaTeX: \displaystyle x = 68$ , in the original equation gives $LaTeX: \displaystyle 10 = 6$ which is false so it is an extraneous solution and there is no solution.