[tex] \sqrt{2x+3} = x + 2 \\ \\ 2x + 3 = (x + 2)^2 \ / \ square \ each \ side \\ \\ 2x + 3 = x^2 + 4x + 4 \ / \ expand \\ \\ 2x + 3 - x^2 - 4x - 4 = 0 \ / \ move \ terms \\ \\ -2x + 3 - x^2 - 4 = 0 \ / \ simplify \\ \\ -2x - x^2 - 1 = - \ / \ simplify \\ \\ x^2 + 2x + 1 = 0 \ / \ multiply \ each \ side \ by \ -1 \\ \\ x^2 + 2(x)(1) + 1^2 = 0 \ / \ rewrite \\ \\ (x + 1)^2 = 0 \ / \ square \ of \ sum \\ \\ x + 1 = 0 \ / \ square \ root \ of \ each \ side \\ \\ x = -1 \ / \ subtract \ 1 \ from \ each \ side \\ \\ [/tex]
The final result is x = -1.
