Solve m^2+16=0

$$m ^ { 2 } + 16 = 0$$

Solve for m

$$m=-4i$$

$$m=4i$$

Steps by Finding Square Root

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$m^{2}=-16$$

The equation is now solved.

$$m=4i m=-4i$$

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.

$$m^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 16}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 16}}{2}$$

Multiply -4 times 16.

$$m=\frac{0±\sqrt{-64}}{2}$$

Take the square root of -64.

$$m=\frac{0±8i}{2}$$

Now solve the equation m=\frac{0±8i}{2} when ± is plus.

$$m=4i$$

Now solve the equation m=\frac{0±8i}{2} when ± is minus.

$$m=-4i$$

The equation is now solved.

$$m=4i m=-4i$$