Solve m^2=-75

$$m ^ { 2 } = - 75$$

Solve for m

$$m=-5\sqrt{3}i\approx -0-8.660254038i$$

$$m=5\sqrt{3}i\approx 8.660254038i$$

Steps by Finding Square Root

The equation is now solved.

$$m=5\sqrt{3}i m=-5\sqrt{3}i$$

Steps Using the Quadratic Formula

Add 75 to both sides.

$$m^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 75}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 75}}{2}$$

Multiply -4 times 75.

$$m=\frac{0±\sqrt{-300}}{2}$$

Take the square root of -300.

$$m=\frac{0±10\sqrt{3}i}{2}$$

Now solve the equation m=\frac{0±10\sqrt{3}i}{2} when ± is plus.

$$m=5\sqrt{3}i$$

Now solve the equation m=\frac{0±10\sqrt{3}i}{2} when ± is minus.

$$m=-5\sqrt{3}i$$

The equation is now solved.

$$m=5\sqrt{3}i m=-5\sqrt{3}i$$