Solve 3(x+2)^2=54

$$3 ( x + 2 ) ^ { 2 } = 54$$

Solve for x

$$x=3\sqrt{2}-2\approx 2.242640687$$

$$x=-3\sqrt{2}-2\approx -6.242640687$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{3\left(x+2\right)^{2}}{3}=\frac{54}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x+2\right)^{2}=\frac{54}{3}$$

Divide 54 by 3.

$$\left(x+2\right)^{2}=18$$

Take the square root of both sides of the equation.

$$x+2=3\sqrt{2} x+2=-3\sqrt{2}$$

Subtract 2 from both sides of the equation.

$$x+2-2=3\sqrt{2}-2 x+2-2=-3\sqrt{2}-2$$

Subtracting 2 from itself leaves 0.

$$x=3\sqrt{2}-2 x=-3\sqrt{2}-2$$