Solve. $LaTeX: \displaystyle \sqrt{x + 22}=\sqrt{x - 4} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 22=x + 6 \sqrt{x - 4} + 5$ . Isolating the radical gives $LaTeX: \displaystyle \frac{17}{6}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{289}{36}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{433}{36}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{433}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{35}{6} = \frac{35}{6}$ which is true so the solution checks.