Solve. $LaTeX: \displaystyle \sqrt{x + 24}=\sqrt{x + 8} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 24=x + 8 \sqrt{x + 8} + 24$ . Isolating the radical gives $LaTeX: \displaystyle 0=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle 0=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=-8$ . Checking the solution, $LaTeX: \displaystyle x = -8$ , in the original equation gives $LaTeX: \displaystyle 4 = 4$ which is true so the solution checks.