Solve n^2+8=80

$$n ^ { 2 } + 8 = 80$$

Solve for n

$$n=6\sqrt{2}\approx 8.485281374$$

$$n=-6\sqrt{2}\approx -8.485281374$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$n^{2}=80-8$$

Subtract 8 from 80 to get 72.

$$n^{2}=72$$

Take the square root of both sides of the equation.

$$n=6\sqrt{2} n=-6\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 80 from both sides.

$$n^{2}+8-80=0$$

Subtract 80 from 8 to get -72.

$$n^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-72\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-72\right)}}{2}$$

Multiply -4 times -72.

$$n=\frac{0±\sqrt{288}}{2}$$

Take the square root of 288.

$$n=\frac{0±12\sqrt{2}}{2}$$

Now solve the equation n=\frac{0±12\sqrt{2}}{2} when ± is plus.

$$n=6\sqrt{2}$$

Now solve the equation n=\frac{0±12\sqrt{2}}{2} when ± is minus.

$$n=-6\sqrt{2}$$

The equation is now solved.

$$n=6\sqrt{2} n=-6\sqrt{2}$$