Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x - 4} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x + 4 \sqrt{x - 4}$ . Isolating the radical gives $LaTeX: \displaystyle \frac{13}{2}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{169}{4}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{185}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{185}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{17}{2} = \frac{17}{2}$ which is true so the solution checks.