Solve 6m^2=-414

$$6 m ^ { 2 } = - 414$$

Solve for m

$$m=-\sqrt{69}i\approx -0-8.306623863i$$

$$m=\sqrt{69}i\approx 8.306623863i$$

Steps by Finding Square Root

Divide both sides by 6.

$$m^{2}=\frac{-414}{6}$$

Divide -414 by 6 to get -69.

$$m^{2}=-69$$

The equation is now solved.

$$m=\sqrt{69}i m=-\sqrt{69}i$$

Steps Using the Quadratic Formula

Divide both sides by 6.

$$m^{2}=\frac{-414}{6}$$

Divide -414 by 6 to get -69.

$$m^{2}=-69$$

Add 69 to both sides.

$$m^{2}+69=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 69 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 69}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 69}}{2}$$

Multiply -4 times 69.

$$m=\frac{0±\sqrt{-276}}{2}$$

Take the square root of -276.

$$m=\frac{0±2\sqrt{69}i}{2}$$

Now solve the equation m=\frac{0±2\sqrt{69}i}{2} when ± is plus.

$$m=\sqrt{69}i$$

Now solve the equation m=\frac{0±2\sqrt{69}i}{2} when ± is minus.

$$m=-\sqrt{69}i$$

The equation is now solved.

$$m=\sqrt{69}i m=-\sqrt{69}i$$