Solve. $LaTeX: \displaystyle \sqrt{x + 24}=\sqrt{x - 4} - 3$

Squaring both sides gives $LaTeX: \displaystyle x + 24=x - 6 \sqrt{x - 4} + 5$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{19}{6}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{361}{36}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{505}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{505}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{37}{6} = \frac{1}{6}$ which is false so it is an extraneous solution and there is no solution.