Solve. $LaTeX: \displaystyle \sqrt{x + 28}=\sqrt{x + 2} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 28=x + 6 \sqrt{x + 2} + 11$ . Isolating the radical gives $LaTeX: \displaystyle \frac{17}{6}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{289}{36}=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{217}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{217}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{35}{6} = \frac{35}{6}$ which is true so the solution checks.