Solve x^2-8k-33=0

$$x ^ { 2 } - 8 k - 33 = 0$$

Solve for k

$$k=\frac{x^{2}-33}{8}$$

Steps for Solving Linear Equation

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

$$-8k-33=-x^{2}$$

Add 33 to both sides.

$$-8k=-x^{2}+33$$

The equation is in standard form.

$$-8k=33-x^{2}$$

Divide both sides by -8.

$$\frac{-8k}{-8}=\frac{33-x^{2}}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$k=\frac{33-x^{2}}{-8}$$

Divide -x^{2}+33 by -8.

$$k=\frac{x^{2}-33}{8}$$

Solve for x (complex solution)

$$x=-\sqrt{8k+33}$$

$$x=\sqrt{8k+33}$$

Solve for x

$$x=\sqrt{8k+33}$$

$$x=-\sqrt{8k+33}\text{, }k\geq -\frac{33}{8}$$