Solve x^2-7x-2c=0

$$x ^ { 2 } - 7 x - 2 c = 0$$

Solve for c

$$c=\frac{x\left(x-7\right)}{2}$$

Steps for Solving Linear Equation

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

$$-7x-2c=-x^{2}$$

Add 7x to both sides.

$$-2c=-x^{2}+7x$$

The equation is in standard form.

$$-2c=7x-x^{2}$$

Divide both sides by -2.

$$\frac{-2c}{-2}=\frac{x\left(7-x\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$c=\frac{x\left(7-x\right)}{-2}$$

Divide x\left(7-x\right) by -2.

$$c=-\frac{x\left(7-x\right)}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8c+49}+7}{2}$$

$$x=\frac{-\sqrt{8c+49}+7}{2}$$

Solve for x

$$x=\frac{\sqrt{8c+49}+7}{2}$$

$$x=\frac{-\sqrt{8c+49}+7}{2}\text{, }c\geq -\frac{49}{8}$$