Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x + 8} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x + 4 \sqrt{x + 8} + 12$ . Isolating the radical gives $LaTeX: \displaystyle \frac{7}{2}=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle \frac{49}{4}=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{17}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{17}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{11}{2} = \frac{11}{2}$ which is true so the solution checks.