Solve x^2+2=108

$$x ^ { 2 } + 2 = 108$$

Solve for x

$$x=\sqrt{106}\approx 10.295630141$$

$$x=-\sqrt{106}\approx -10.295630141$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$x^{2}=108-2$$

Subtract 2 from 108 to get 106.

$$x^{2}=106$$

Take the square root of both sides of the equation.

$$x=\sqrt{106} x=-\sqrt{106}$$

Steps Using the Quadratic Formula

Subtract 108 from both sides.

$$x^{2}+2-108=0$$

Subtract 108 from 2 to get -106.

$$x^{2}-106=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -106 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-106\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-106\right)}}{2}$$

Multiply -4 times -106.

$$x=\frac{0±\sqrt{424}}{2}$$

Take the square root of 424.

$$x=\frac{0±2\sqrt{106}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{106}}{2} when ± is plus.

$$x=\sqrt{106}$$

Now solve the equation x=\frac{0±2\sqrt{106}}{2} when ± is minus.

$$x=-\sqrt{106}$$

The equation is now solved.

$$x=\sqrt{106} x=-\sqrt{106}$$