Solve -2x^2=1

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Steps by Finding Square Root

Divide both sides by -2.

$$x^{2}=-\frac{1}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{2}i}{2} x=-\frac{\sqrt{2}i}{2}$$

Steps Using the Quadratic Formula

Divide both sides by -2.

$$x^{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides.

$$x^{2}+\frac{1}{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}}}{2}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{0±\sqrt{-2}}{2}$$

Take the square root of -2.

$$x=\frac{0±\sqrt{2}i}{2}$$

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

$$x=\frac{\sqrt{2}i}{2}$$

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

$$x=-\frac{\sqrt{2}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{2}i}{2} x=-\frac{\sqrt{2}i}{2}$$