Solve 9x^2-2=0

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

Solve for x

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

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

Steps by Finding Square Root

Add 2 to both sides. Anything plus zero gives itself.

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

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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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

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

Square 0.

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

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-2\right)}}{2\times 9}$$

Multiply -36 times -2.

$$x=\frac{0±\sqrt{72}}{2\times 9}$$

Take the square root of 72.

$$x=\frac{0±6\sqrt{2}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6\sqrt{2}}{18}$$

Now solve the equation x=\frac{0±6\sqrt{2}}{18} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{2}}{18} when ± is minus.

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

The equation is now solved.

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