Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x - 6} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x + 8 \sqrt{x - 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle \frac{3}{4}=\sqrt{x - 6}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{16}=x - 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{105}{16}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{105}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{19}{4} = \frac{19}{4}$ which is true so the solution checks.