Solve 2x^2+10=0

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

Solve for x (complex solution)

$$x=-\sqrt{5}i\approx -0-2.236067977i$$

$$x=\sqrt{5}i\approx 2.236067977i$$

Steps by Finding Square Root

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

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

Divide both sides by 2.

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

Divide -10 by 2 to get -5.

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

The equation is now solved.

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

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 10}}{2\times 2}$$

Multiply -8 times 10.

$$x=\frac{0±\sqrt{-80}}{2\times 2}$$

Take the square root of -80.

$$x=\frac{0±4\sqrt{5}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{5}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{5}i}{4} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{5}i}{4} when ± is minus.

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

The equation is now solved.

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