Solve 4m^2-2mx+c=4m

$$4 m ^ { 2 } - 2 m x + c = 4 m$$

Solve for c

$$c=-2m\left(-x+2m-2\right)$$

Solution Steps

Subtract 4m^{2} from both sides.

$$-2mx+c=4m-4m^{2}$$

Add 2mx to both sides.

$$c=4m-4m^{2}+2mx$$

Solve for m (complex solution)

$$m=\frac{\sqrt{x^{2}+4x-4c+4}+x+2}{4}$$

$$m=\frac{-\sqrt{x^{2}+4x-4c+4}+x+2}{4}$$

Solve for m

$$m=\frac{\sqrt{x^{2}+4x-4c+4}+x+2}{4}$$

$$m=\frac{-\sqrt{x^{2}+4x-4c+4}+x+2}{4}\text{, }c\leq \frac{\left(x+2\right)^{2}}{4}$$