Solve. $LaTeX: \displaystyle \sqrt{x + 12}=\sqrt{x + 2} - 3$

Squaring both sides gives $LaTeX: \displaystyle x + 12=x - 6 \sqrt{x + 2} + 11$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{1}{6}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{1}{36}=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{71}{36}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{71}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{19}{6} = - \frac{17}{6}$ which is false so it is an extraneous solution and there is no solution.