Solve. $LaTeX: \displaystyle \sqrt{x + 22}=\sqrt{x + 6} - 3$

Squaring both sides gives $LaTeX: \displaystyle x + 22=x - 6 \sqrt{x + 6} + 15$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{7}{6}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{49}{36}=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{167}{36}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{167}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{25}{6} = - \frac{11}{6}$ which is false so it is an extraneous solution and there is no solution.