Solve 12(x-2)^2=9

$$12 ( x - 2 ) ^ { 2 } = 9$$

Solve for x

$$x=\frac{\sqrt{3}}{2}+2\approx 2.866025404$$

$$x=-\frac{\sqrt{3}}{2}+2\approx 1.133974596$$

Steps by Finding Square Root

Divide both sides by 12.

$$\frac{12\left(x-2\right)^{2}}{12}=\frac{9}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$\left(x-2\right)^{2}=\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\left(x-2\right)^{2}=\frac{3}{4}$$

Take the square root of both sides of the equation.

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

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{\sqrt{3}}{2}-\left(-2\right) x-2-\left(-2\right)=-\frac{\sqrt{3}}{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{\sqrt{3}}{2}-\left(-2\right) x=-\frac{\sqrt{3}}{2}-\left(-2\right)$$

Subtract -2 from \frac{\sqrt{3}}{2}.

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

Subtract -2 from -\frac{\sqrt{3}}{2}.

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

The equation is now solved.

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