Solve 12-2x^2=0

$$12 - 2 x ^ { 2 } = 0$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-2x^{2}=-12$$

Divide both sides by -2.

$$x^{2}=\frac{-12}{-2}$$

Divide -12 by -2 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

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.

$$-2x^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 12}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 12}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 12}}{2\left(-2\right)}$$

Multiply 8 times 12.

$$x=\frac{0±\sqrt{96}}{2\left(-2\right)}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{6}}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{-4} when ± is plus.

$$x=-\sqrt{6}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{-4} when ± is minus.

$$x=\sqrt{6}$$

The equation is now solved.

$$x=-\sqrt{6} x=\sqrt{6}$$