Solve x^2=33

$$x ^ { 2 } = 33$$

Solve for x

$$x=\sqrt{33}\approx 5.744562647$$

$$x=-\sqrt{33}\approx -5.744562647$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\sqrt{33} x=-\sqrt{33}$$

Steps Using the Quadratic Formula

Subtract 33 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -33 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-33\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-33\right)}}{2}$$

Multiply -4 times -33.

$$x=\frac{0±\sqrt{132}}{2}$$

Take the square root of 132.

$$x=\frac{0±2\sqrt{33}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{33}}{2} when ± is plus.

$$x=\sqrt{33}$$

Now solve the equation x=\frac{0±2\sqrt{33}}{2} when ± is minus.

$$x=-\sqrt{33}$$

The equation is now solved.

$$x=\sqrt{33} x=-\sqrt{33}$$