Solve. $LaTeX: \displaystyle \sqrt{x + 28}=\sqrt{x - 4} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 28=x + 8 \sqrt{x - 4} + 12$ . Isolating the radical gives $LaTeX: \displaystyle 2=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle 4=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=8$ . Checking the solution, $LaTeX: \displaystyle x = 8$ , in the original equation gives $LaTeX: \displaystyle 6 = 6$ which is true so the solution checks.