Solve 5x^2+2+1=0

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{15}i}{5}\approx -0-0.774596669i$$

$$x=\frac{\sqrt{15}i}{5}\approx 0.774596669i$$

Steps by Finding Square Root

Add 2 and 1 to get 3.

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

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by 5.

$$x^{2}=-\frac{3}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{15}i}{5} x=-\frac{\sqrt{15}i}{5}$$

Steps Using the Quadratic Formula

Add 2 and 1 to get 3.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 3}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 3}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 3}}{2\times 5}$$

Multiply -20 times 3.

$$x=\frac{0±\sqrt{-60}}{2\times 5}$$

Take the square root of -60.

$$x=\frac{0±2\sqrt{15}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{15}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{10} when ± is plus.

$$x=\frac{\sqrt{15}i}{5}$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{10} when ± is minus.

$$x=-\frac{\sqrt{15}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{15}i}{5} x=-\frac{\sqrt{15}i}{5}$$