Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x - 4} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x - 4 \sqrt{x - 4}$ . Isolating the radical gives $LaTeX: \displaystyle -4=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle 16=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=20$ . Checking the solution, $LaTeX: \displaystyle x = 20$ , in the original equation gives $LaTeX: \displaystyle 6 = 2$ which is false so it is an extraneous solution and there is no solution.