Solve x^2-120=0

$$x ^ { 2 } - 120 = 0$$

Solve for x

$$x=2\sqrt{30}\approx 10.95445115$$

$$x=-2\sqrt{30}\approx -10.95445115$$

Steps by Finding Square Root

Add 120 to both sides. Anything plus zero gives itself.

$$x^{2}=120$$

Take the square root of both sides of the equation.

$$x=2\sqrt{30} x=-2\sqrt{30}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-120=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -120 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-120\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-120\right)}}{2}$$

Multiply -4 times -120.

$$x=\frac{0±\sqrt{480}}{2}$$

Take the square root of 480.

$$x=\frac{0±4\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{30}}{2} when ± is plus.

$$x=2\sqrt{30}$$

Now solve the equation x=\frac{0±4\sqrt{30}}{2} when ± is minus.

$$x=-2\sqrt{30}$$

The equation is now solved.

$$x=2\sqrt{30} x=-2\sqrt{30}$$