Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x - 6} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x + 2 \sqrt{x - 6} - 5$ . Isolating the radical gives $LaTeX: \displaystyle \frac{31}{2}=\sqrt{x - 6}$ Squaring again gives $LaTeX: \displaystyle \frac{961}{4}=x - 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{985}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{985}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{33}{2} = \frac{33}{2}$ which is true so the solution checks.