Solve $LaTeX: \displaystyle x + 5 = \sqrt{9 x + 115}$ .

Squaring both sides gives $LaTeX: \displaystyle x^{2} + 10 x + 25 = 9 x + 115$ . The equation is quadratic setting it equal to zero gives $LaTeX: \displaystyle x^{2} + x - 90 = 0$ . Factoring gives $LaTeX: \displaystyle (x - 9)(x + 10)=0$ so the possible solutions are $LaTeX: \displaystyle x = 9$ and $LaTeX: \displaystyle x = -10$ . Checking the solution $LaTeX: \displaystyle x = 9$ in the original equation gives $LaTeX: \displaystyle 14 = 14$ . The solution checks, so $LaTeX: \displaystyle x = 9$ is a true solution. Checking the solution $LaTeX: \displaystyle x = -10$ in the original equation gives $LaTeX: \displaystyle -5 = 5$ . The solution does no check, so $LaTeX: \displaystyle x = -10$ is an extraneous solution.