Solve. $LaTeX: \displaystyle \sqrt{x + 18}=\sqrt{x - 2} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 18=x - 4 \sqrt{x - 2} + 2$ . Isolating the radical gives $LaTeX: \displaystyle -4=\sqrt{x - 2}$ Squaring again gives $LaTeX: \displaystyle 16=x - 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=18$ . Checking the solution, $LaTeX: \displaystyle x = 18$ , in the original equation gives $LaTeX: \displaystyle 6 = 2$ which is false so it is an extraneous solution and there is no solution.