Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x + 4} - 1$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x - 2 \sqrt{x + 4} + 5$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{21}{2}=\sqrt{x + 4}$ Squaring again gives $LaTeX: \displaystyle \frac{441}{4}=x + 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{425}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{425}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{23}{2} = \frac{19}{2}$ which is false so it is an extraneous solution and there is no solution.