Solve. $LaTeX: \displaystyle \sqrt{x + 18}=\sqrt{x + 2} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 18=x + 8 \sqrt{x + 2} + 18$ . Isolating the radical gives $LaTeX: \displaystyle 0=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle 0=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=-2$ . Checking the solution, $LaTeX: \displaystyle x = -2$ , in the original equation gives $LaTeX: \displaystyle 4 = 4$ which is true so the solution checks.