Answer
$12$
Work Step by Step
$\sqrt{4x-23}-3=2$
Add $3$ to both sides:
$\sqrt{4x-23}-3+3=2+3$
$\sqrt{4x-23}=5$
Square both sides:
$(\sqrt{4x-23})^2=(5)^2$
$4x-23=25$
Add $23$ to both sides:
$4x-23+23=25+23$
$4x=48$
Divide both sides by $4$:
$$\frac{4x}{4}=\frac{48}{4}$$
$x=12$
Substitute into original problem to check for extraneous solutions:
$\sqrt{4(12)-23}-3=2$
$\sqrt{48-23}-3=2$
$\sqrt{25}-3=2$
$5-3=2$
$2=2$
