Solve 0=5x^2+10

$$0 = 5 x ^ { 2 } + 10$$

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$5x^{2}=-10$$

Divide both sides by 5.

$$x^{2}=\frac{-10}{5}$$

Divide -10 by 5 to get -2.

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

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 10}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 10}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 10}}{2\times 5}$$

Multiply -20 times 10.

$$x=\frac{0±\sqrt{-200}}{2\times 5}$$

Take the square root of -200.

$$x=\frac{0±10\sqrt{2}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{2}i}{10}$$

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

$$x=\sqrt{2}i$$

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

$$x=-\sqrt{2}i$$

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$