Solve 2-9x^2=0

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

Solve for x

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

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

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -9.

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

Fraction \frac{-2}{-9} can be simplified to \frac{2}{9} by removing the negative sign from both the numerator and the denominator.

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

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}.

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

Square 0.

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

Multiply -4 times -9.

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

Multiply 36 times 2.

$$x=\frac{0±\sqrt{72}}{2\left(-9\right)}$$

Take the square root of 72.

$$x=\frac{0±6\sqrt{2}}{2\left(-9\right)}$$

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.

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