Solve 10x^2-2c-10=0

$$10 { x }^{ 2 } -2c-10=0$$

Solve for c

$$c=5\left(x^{2}-1\right)$$

Steps for Solving Linear Equation

Subtract 10x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2c-10=-10x^{2}$$

Add 10 to both sides.

$$-2c=-10x^{2}+10$$

The equation is in standard form.

$$-2c=10-10x^{2}$$

Divide both sides by -2.

$$\frac{-2c}{-2}=\frac{10-10x^{2}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$c=\frac{10-10x^{2}}{-2}$$

Divide -10x^{2}+10 by -2.

$$c=5x^{2}-5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{5\left(c+5\right)}}{5}$$

$$x=\frac{\sqrt{5\left(c+5\right)}}{5}$$

Solve for x

$$x=\frac{\sqrt{5\left(c+5\right)}}{5}$$

$$x=-\frac{\sqrt{5\left(c+5\right)}}{5}\text{, }c\geq -5$$