Solve 5x^2+2=0

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

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

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

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

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.

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

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.

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