Solve 5m^2+2m+k=0

$$5 m ^ { 2 } + 2 m + k = 0$$

Solve for k

$$k=-m\left(5m+2\right)$$

Solution Steps

Subtract 5m^{2} from both sides. Anything subtracted from zero gives its negation.

$$2m+k=-5m^{2}$$

Subtract 2m from both sides.

$$k=-5m^{2}-2m$$

Solve for m

$$m=\frac{\sqrt{1-5k}-1}{5}$$

$$m=\frac{-\sqrt{1-5k}-1}{5}\text{, }k\leq \frac{1}{5}$$