Solve. $LaTeX: \displaystyle \sqrt{x + 30}=\sqrt{x - 8} - 3$

Squaring both sides gives $LaTeX: \displaystyle x + 30=x - 6 \sqrt{x - 8} + 1$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{29}{6}=\sqrt{x - 8}$ Squaring again gives $LaTeX: \displaystyle \frac{841}{36}=x - 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{1129}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{1129}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{47}{6} = \frac{11}{6}$ which is false so it is an extraneous solution and there is no solution.