Solve. $LaTeX: \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 30=x + 2 \sqrt{x + 6} + 7$ . Isolating the radical gives $LaTeX: \displaystyle \frac{23}{2}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{529}{4}=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{505}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{505}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{25}{2} = \frac{25}{2}$ which is true so the solution checks.