Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x - 4} - 3$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x - 6 \sqrt{x - 4} + 5$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{11}{6}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{121}{36}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{265}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{265}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{29}{6} = - \frac{7}{6}$ which is false so it is an extraneous solution and there is no solution.