Solve 12-2x^2=-16

$$12 - 2 x ^ { 2 } = - 16$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Subtract 12 from both sides.

$$-2x^{2}=-16-12$$

Subtract 12 from -16 to get -28.

$$-2x^{2}=-28$$

Divide both sides by -2.

$$x^{2}=\frac{-28}{-2}$$

Divide -28 by -2 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Add 16 to both sides.

$$12-2x^{2}+16=0$$

Add 12 and 16 to get 28.

$$28-2x^{2}=0$$

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.

$$-2x^{2}+28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 28}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 28}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 28}}{2\left(-2\right)}$$

Multiply 8 times 28.

$$x=\frac{0±\sqrt{224}}{2\left(-2\right)}$$

Take the square root of 224.

$$x=\frac{0±4\sqrt{14}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{14}}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{14}}{-4} when ± is plus.

$$x=-\sqrt{14}$$

Now solve the equation x=\frac{0±4\sqrt{14}}{-4} when ± is minus.

$$x=\sqrt{14}$$

The equation is now solved.

$$x=-\sqrt{14} x=\sqrt{14}$$