Solve 33x^2=9

$$33 x ^ { 2 } = 9$$

Solve for x

$$x=\frac{\sqrt{33}}{11}\approx 0.522232968$$

$$x=-\frac{\sqrt{33}}{11}\approx -0.522232968$$

Steps by Finding Square Root

Divide both sides by 33.

$$x^{2}=\frac{9}{33}$$

Reduce the fraction \frac{9}{33} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{3}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{33}}{11} x=-\frac{\sqrt{33}}{11}$$

Steps Using the Quadratic Formula

Divide both sides by 33.

$$x^{2}=\frac{9}{33}$$

Reduce the fraction \frac{9}{33} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{3}{11}$$

Subtract \frac{3}{11} from both sides.

$$x^{2}-\frac{3}{11}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{11} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{11}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{11}\right)}}{2}$$

Multiply -4 times -\frac{3}{11}.

$$x=\frac{0±\sqrt{\frac{12}{11}}}{2}$$

Take the square root of \frac{12}{11}.

$$x=\frac{0±\frac{2\sqrt{33}}{11}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{33}}{11}}{2} when ± is plus.

$$x=\frac{\sqrt{33}}{11}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{33}}{11}}{2} when ± is minus.

$$x=-\frac{\sqrt{33}}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{33}}{11} x=-\frac{\sqrt{33}}{11}$$