Solve 20x^2+3=1

$$20 x ^ { 2 } + 3 = 1$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10}i}{10}\approx -0-0.316227766i$$

$$x=\frac{\sqrt{10}i}{10}\approx 0.316227766i$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$20x^{2}=1-3$$

Subtract 3 from 1 to get -2.

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

Divide both sides by 20.

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

Reduce the fraction \frac{-2}{20} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{1}{10}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$20x^{2}+3-1=0$$

Subtract 1 from 3 to get 2.

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

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

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

Square 0.

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

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\times 2}}{2\times 20}$$

Multiply -80 times 2.

$$x=\frac{0±\sqrt{-160}}{2\times 20}$$

Take the square root of -160.

$$x=\frac{0±4\sqrt{10}i}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±4\sqrt{10}i}{40}$$

Now solve the equation x=\frac{0±4\sqrt{10}i}{40} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{10}i}{40} when ± is minus.

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

The equation is now solved.

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