Solve. $LaTeX: \displaystyle \sqrt{x + 30}=\sqrt{x - 6} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 30=x + 8 \sqrt{x - 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle \frac{5}{2}=\sqrt{x - 6}$ Squaring again gives $LaTeX: \displaystyle \frac{25}{4}=x - 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{49}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{49}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{13}{2} = \frac{13}{2}$ which is true so the solution checks.