Solve 20x^2+1=0

$$20 { x }^{ 2 } +1=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{5}i}{10}\approx -0-0.223606798i$$

$$x=\frac{\sqrt{5}i}{10}\approx 0.223606798i$$

Steps by Finding Square Root

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

$$20x^{2}=-1$$

Divide both sides by 20.

$$x^{2}=-\frac{1}{20}$$

The equation is now solved.

$$x=\frac{\sqrt{5}i}{10} x=-\frac{\sqrt{5}i}{10}$$

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.

$$20x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80}}{2\times 20}$$

Take the square root of -80.

$$x=\frac{0±4\sqrt{5}i}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±4\sqrt{5}i}{40}$$

Now solve the equation x=\frac{0±4\sqrt{5}i}{40} when ± is plus.

$$x=\frac{\sqrt{5}i}{10}$$

Now solve the equation x=\frac{0±4\sqrt{5}i}{40} when ± is minus.

$$x=-\frac{\sqrt{5}i}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{5}i}{10} x=-\frac{\sqrt{5}i}{10}$$