Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x + 6} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x + 4 \sqrt{x + 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle \frac{3}{2}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{4}=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{15}{4}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{15}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{7}{2} = \frac{7}{2}$ which is true so the solution checks.