Solve 12(2-x)^2-9=0

$$12 ( 2 - x ) ^ { 2 } - 9 = 0$$

Solve for x

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

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

Steps by Finding Square Root

Add 9 to both sides of the equation.

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

Subtracting 9 from itself leaves 0.

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

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.

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

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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

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

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

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

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

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{\sqrt{3}}{2}-2}{-1} \frac{-x}{-1}=\frac{-\frac{\sqrt{3}}{2}-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{\sqrt{3}}{2}-2}{-1} x=\frac{-\frac{\sqrt{3}}{2}-2}{-1}$$

Divide \frac{\sqrt{3}}{2}-2 by -1.

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

Divide -\frac{\sqrt{3}}{2}-2 by -1.

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

The equation is now solved.

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