Solve. $LaTeX: \displaystyle \sqrt{x + 12}=\sqrt{x + 8} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 12=x + 2 \sqrt{x + 8} + 9$ . Isolating the radical gives $LaTeX: \displaystyle \frac{3}{2}=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{4}=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{23}{4}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{23}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{5}{2} = \frac{5}{2}$ which is true so the solution checks.