Solve 1+2x^2=0

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

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

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

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

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8}}{2\times 2}$$

Take the square root of -8.

$$x=\frac{0±2\sqrt{2}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{2}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{4} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{2}i}{4} when ± is minus.

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

The equation is now solved.

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