Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x - 2} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x + 2 \sqrt{x - 2} - 1$ . Isolating the radical gives $LaTeX: \displaystyle \frac{27}{2}=\sqrt{x - 2}$ Squaring again gives $LaTeX: \displaystyle \frac{729}{4}=x - 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{737}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{737}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{29}{2} = \frac{29}{2}$ which is true so the solution checks.