Solve. $LaTeX: \displaystyle \sqrt{x + 22}=\sqrt{x + 4} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 22=x + 2 \sqrt{x + 4} + 5$ . Isolating the radical gives $LaTeX: \displaystyle \frac{17}{2}=\sqrt{x + 4}$ Squaring again gives $LaTeX: \displaystyle \frac{289}{4}=x + 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{273}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{273}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{19}{2} = \frac{19}{2}$ which is true so the solution checks.