Solve 6(x+2)^2=9

$$6 ( x + 2 ) ^ { 2 } = 9$$

Solve for x

$$x=\frac{\sqrt{6}}{2}-2\approx -0.775255129$$

$$x=-\frac{\sqrt{6}}{2}-2\approx -3.224744871$$

Steps by Finding Square Root

Divide both sides by 6.

$$\frac{6\left(x+2\right)^{2}}{6}=\frac{9}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$\left(x+2\right)^{2}=\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

Take the square root of both sides of the equation.

$$x+2=\frac{\sqrt{6}}{2} x+2=-\frac{\sqrt{6}}{2}$$

Subtract 2 from both sides of the equation.

$$x+2-2=\frac{\sqrt{6}}{2}-2 x+2-2=-\frac{\sqrt{6}}{2}-2$$

Subtracting 2 from itself leaves 0.

$$x=\frac{\sqrt{6}}{2}-2 x=-\frac{\sqrt{6}}{2}-2$$