Solve n^2+8=120

$$n ^ { 2 } + 8 = 120$$

Solve for n

$$n=4\sqrt{7}\approx 10.583005244$$

$$n=-4\sqrt{7}\approx -10.583005244$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$n^{2}=120-8$$

Subtract 8 from 120 to get 112.

$$n^{2}=112$$

Take the square root of both sides of the equation.

$$n=4\sqrt{7} n=-4\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 120 from both sides.

$$n^{2}+8-120=0$$

Subtract 120 from 8 to get -112.

$$n^{2}-112=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -112 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-112\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-112\right)}}{2}$$

Multiply -4 times -112.

$$n=\frac{0±\sqrt{448}}{2}$$

Take the square root of 448.

$$n=\frac{0±8\sqrt{7}}{2}$$

Now solve the equation n=\frac{0±8\sqrt{7}}{2} when ± is plus.

$$n=4\sqrt{7}$$

Now solve the equation n=\frac{0±8\sqrt{7}}{2} when ± is minus.

$$n=-4\sqrt{7}$$

The equation is now solved.

$$n=4\sqrt{7} n=-4\sqrt{7}$$