Solve 1/4x^2+2=0

$$\frac{ 1 }{ 4 } { x }^{ 2 } +2=0$$

Solve for x (complex solution)

$$x=-2\sqrt{2}i\approx -0-2.828427125i$$

$$x=2\sqrt{2}i\approx 2.828427125i$$

Steps by Finding Square Root

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

$$\frac{1}{4}x^{2}=-2$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x^{2}=-2\times 4$$

Multiply -2 and 4 to get -8.

$$x^{2}=-8$$

The equation is now solved.

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

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.

$$\frac{1}{4}x^{2}+2=0$$

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

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

Square 0.

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

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

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

Take the square root of -2.

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

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

$$x=\frac{0±\sqrt{2}i}{\frac{1}{2}}$$

Now solve the equation x=\frac{0±\sqrt{2}i}{\frac{1}{2}} when ± is plus.

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

Now solve the equation x=\frac{0±\sqrt{2}i}{\frac{1}{2}} when ± is minus.

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

The equation is now solved.

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