Solve x^2=125

$${ x }^{ 2 } =125$$

Solve for x

$$x=5\sqrt{5}\approx 11.180339887$$

$$x=-5\sqrt{5}\approx -11.180339887$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=5\sqrt{5} x=-5\sqrt{5}$$

Steps Using the Quadratic Formula

Subtract 125 from both sides.

$$x^{2}-125=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -125 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-125\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-125\right)}}{2}$$

Multiply -4 times -125.

$$x=\frac{0±\sqrt{500}}{2}$$

Take the square root of 500.

$$x=\frac{0±10\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{5}}{2} when ± is plus.

$$x=5\sqrt{5}$$

Now solve the equation x=\frac{0±10\sqrt{5}}{2} when ± is minus.

$$x=-5\sqrt{5}$$

The equation is now solved.

$$x=5\sqrt{5} x=-5\sqrt{5}$$