Solve 5x^2+3=1

$$5 x ^ { 2 } + 3 = 1$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10}i}{5}\approx -0-0.632455532i$$

$$x=\frac{\sqrt{10}i}{5}\approx 0.632455532i$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$5x^{2}=1-3$$

Subtract 3 from 1 to get -2.

$$5x^{2}=-2$$

Divide both sides by 5.

$$x^{2}=-\frac{2}{5}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$5x^{2}+3-1=0$$

Subtract 1 from 3 to get 2.

$$5x^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 2}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 2}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 2}}{2\times 5}$$

Multiply -20 times 2.

$$x=\frac{0±\sqrt{-40}}{2\times 5}$$

Take the square root of -40.

$$x=\frac{0±2\sqrt{10}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{10}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{10}i}{10} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{10}i}{10} when ± is minus.

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

The equation is now solved.

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