Solve -2x^2-8=0

$$- 2 x ^ { 2 } - 8 = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$-2x^{2}=8$$

Divide both sides by -2.

$$x^{2}=\frac{8}{-2}$$

Divide 8 by -2 to get -4.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

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.

$$-2x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-8\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-8\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-8\right)}}{2\left(-2\right)}$$

Multiply 8 times -8.

$$x=\frac{0±\sqrt{-64}}{2\left(-2\right)}$$

Take the square root of -64.

$$x=\frac{0±8i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±8i}{-4}$$

Now solve the equation x=\frac{0±8i}{-4} when ± is plus.

$$x=-2i$$

Now solve the equation x=\frac{0±8i}{-4} when ± is minus.

$$x=2i$$

The equation is now solved.

$$x=-2i x=2i$$