Answer
$\color{blue}{x=3}$
Work Step by Step
Add $\sqrt{2x+3}$ to both sides to obtain:
$x=\sqrt{2x+3}$
Square both sides to obtain:
$x^2=2x+3$
Move all terms to the left side of the equation.
Note that when a term is transferred to the other side of the equation, its sign changes to its opposite.
$x^2-2x-3=0$
Factor the trinomial to obtain:
$(x-3)(x+1)=0$
Use the zero-factor property by equating each factor to zero.
$x-3=0$ or $x+1=0$
Solve each equation to obtain:
$x=3$ or $x=-1$.
$-1$ cannot be a solution to the equation as $\sqrt{2x+3}$ is never negative.
Thus, the solution to the given equation is: $\color{blue}{x=3}$.
