Solve. $LaTeX: \displaystyle \sqrt{x + 28}=\sqrt{x - 6} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 28=x + 8 \sqrt{x - 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle \frac{9}{4}=\sqrt{x - 6}$ Squaring again gives $LaTeX: \displaystyle \frac{81}{16}=x - 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{177}{16}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{177}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{25}{4} = \frac{25}{4}$ which is true so the solution checks.