Solve c^2+2=0

$$c ^ { 2 } + 2 = 0$$

Solve for c

$$c=-\sqrt{2}i\approx -0-1.414213562i$$

$$c=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$c^{2}=-2$$

The equation is now solved.

$$c=\sqrt{2}i c=-\sqrt{2}i$$

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.

$$c^{2}+2=0$$

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

$$c=\frac{0±\sqrt{0^{2}-4\times 2}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\times 2}}{2}$$

Multiply -4 times 2.

$$c=\frac{0±\sqrt{-8}}{2}$$

Take the square root of -8.

$$c=\frac{0±2\sqrt{2}i}{2}$$

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

$$c=\sqrt{2}i$$

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

$$c=-\sqrt{2}i$$

The equation is now solved.

$$c=\sqrt{2}i c=-\sqrt{2}i$$