Solve m^2+m+n=0

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

Solve for n

$$n=-m\left(m+1\right)$$

Solution Steps

Subtract m^{2} from both sides. Anything subtracted from zero gives its negation.

$$m+n=-m^{2}$$

Subtract m from both sides.

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

Solve for m (complex solution)

$$m=\frac{\sqrt{1-4n}-1}{2}$$

$$m=\frac{-\sqrt{1-4n}-1}{2}$$

Solve for m

$$m=\frac{\sqrt{1-4n}-1}{2}$$

$$m=\frac{-\sqrt{1-4n}-1}{2}\text{, }n\leq \frac{1}{4}$$