Solve -2m^2-6=0

$$- 2 m ^ { 2 } - 6 = 0$$

Solve for m

$$m=-\sqrt{3}i\approx -0-1.732050808i$$

$$m=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Add 6 to both sides. Anything plus zero gives itself.

$$-2m^{2}=6$$

Divide both sides by -2.

$$m^{2}=\frac{6}{-2}$$

Divide 6 by -2 to get -3.

$$m^{2}=-3$$

The equation is now solved.

$$m=\sqrt{3}i m=-\sqrt{3}i$$

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.

$$-2m^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -2.

$$m=\frac{0±\sqrt{8\left(-6\right)}}{2\left(-2\right)}$$

Multiply 8 times -6.

$$m=\frac{0±\sqrt{-48}}{2\left(-2\right)}$$

Take the square root of -48.

$$m=\frac{0±4\sqrt{3}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$m=\frac{0±4\sqrt{3}i}{-4}$$

Now solve the equation m=\frac{0±4\sqrt{3}i}{-4} when ± is plus.

$$m=-\sqrt{3}i$$

Now solve the equation m=\frac{0±4\sqrt{3}i}{-4} when ± is minus.

$$m=\sqrt{3}i$$

The equation is now solved.

$$m=-\sqrt{3}i m=\sqrt{3}i$$