Solve. $LaTeX: \displaystyle \sqrt{x + 24}=\sqrt{x - 4} - 1$

Squaring both sides gives $LaTeX: \displaystyle x + 24=x - 2 \sqrt{x - 4} - 3$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{27}{2}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{729}{4}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{745}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{745}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{29}{2} = \frac{25}{2}$ which is false so it is an extraneous solution and there is no solution.