Solve n^2+2=1

$$n ^ { 2 } + 2 = 1$$

Solve for n

$$n=-i$$

$$n=i$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$n^{2}=1-2$$

Subtract 2 from 1 to get -1.

$$n^{2}=-1$$

The equation is now solved.

$$n=i n=-i$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$n^{2}+2-1=0$$

Subtract 1 from 2 to get 1.

$$n^{2}+1=0$$

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

$$n=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$n=\frac{0±2i}{2}$$

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

$$n=i$$

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

$$n=-i$$

The equation is now solved.

$$n=i n=-i$$