Solve 9x^2=2

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

Solve for x

$$x=\frac{\sqrt{2}}{3}\approx 0.471404521$$

$$x=-\frac{\sqrt{2}}{3}\approx -0.471404521$$

Steps by Finding Square Root

Divide both sides by 9.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 9.

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

Subtract \frac{2}{9} from both sides.

$$x^{2}-\frac{2}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{9}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2}{9}\right)}}{2}$$

Multiply -4 times -\frac{2}{9}.

$$x=\frac{0±\sqrt{\frac{8}{9}}}{2}$$

Take the square root of \frac{8}{9}.

$$x=\frac{0±\frac{2\sqrt{2}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{2}}{3}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{2\sqrt{2}}{3}}{2} when ± is minus.

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

The equation is now solved.

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