Solve 5left(x+3right)^2-12=13

$$5 { \left(x+3 \right) }^{ 2 } -12=13$$

Solve for x

$$x=\sqrt{5}-3\approx -0.763932023$$

$$x=-\left(\sqrt{5}+3\right)\approx -5.236067977$$

Steps by Finding Square Root

Add 12 to both sides of the equation.

$$5\left(x+3\right)^{2}-12+12=13+12$$

Subtracting 12 from itself leaves 0.

$$5\left(x+3\right)^{2}=13+12$$

Add 13 to 12.

$$5\left(x+3\right)^{2}=25$$

Divide both sides by 5.

$$\frac{5\left(x+3\right)^{2}}{5}=\frac{25}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\left(x+3\right)^{2}=\frac{25}{5}$$

Divide 25 by 5.

$$\left(x+3\right)^{2}=5$$

Take the square root of both sides of the equation.

$$x+3=\sqrt{5} x+3=-\sqrt{5}$$

Subtract 3 from both sides of the equation.

$$x+3-3=\sqrt{5}-3 x+3-3=-\sqrt{5}-3$$

Subtracting 3 from itself leaves 0.

$$x=\sqrt{5}-3 x=-\sqrt{5}-3$$