Solve x^2-114=0

$$x ^ { 2 } - 114 = 0$$

Solve for x

$$x=\sqrt{114}\approx 10.677078252$$

$$x=-\sqrt{114}\approx -10.677078252$$

Steps by Finding Square Root

Add 114 to both sides. Anything plus zero gives itself.

$$x^{2}=114$$

Take the square root of both sides of the equation.

$$x=\sqrt{114} x=-\sqrt{114}$$

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.

$$x^{2}-114=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -114 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-114\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-114\right)}}{2}$$

Multiply -4 times -114.

$$x=\frac{0±\sqrt{456}}{2}$$

Take the square root of 456.

$$x=\frac{0±2\sqrt{114}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{114}}{2} when ± is plus.

$$x=\sqrt{114}$$

Now solve the equation x=\frac{0±2\sqrt{114}}{2} when ± is minus.

$$x=-\sqrt{114}$$

The equation is now solved.

$$x=\sqrt{114} x=-\sqrt{114}$$