Solve. $LaTeX: \displaystyle \sqrt{x + 30}=\sqrt{x + 6} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 30=x + 4 \sqrt{x + 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle 5=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle 25=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=19$ . Checking the solution, $LaTeX: \displaystyle x = 19$ , in the original equation gives $LaTeX: \displaystyle 7 = 7$ which is true so the solution checks.