Solve 2x^2=-512

$$2 x ^ { 2 } = - 512$$

Solve for x (complex solution)

$$x=-16i$$

$$x=16i$$

Steps by Finding Square Root

Divide both sides by 2.

$$x^{2}=\frac{-512}{2}$$

Divide -512 by 2 to get -256.

$$x^{2}=-256$$

The equation is now solved.

$$x=16i x=-16i$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$x^{2}=\frac{-512}{2}$$

Divide -512 by 2 to get -256.

$$x^{2}=-256$$

Add 256 to both sides.

$$x^{2}+256=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 256 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 256}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 256}}{2}$$

Multiply -4 times 256.

$$x=\frac{0±\sqrt{-1024}}{2}$$

Take the square root of -1024.

$$x=\frac{0±32i}{2}$$

Now solve the equation x=\frac{0±32i}{2} when ± is plus.

$$x=16i$$

Now solve the equation x=\frac{0±32i}{2} when ± is minus.

$$x=-16i$$

The equation is now solved.

$$x=16i x=-16i$$