Solve -2x^2-5=0

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{10}i}{2}\approx -0-1.58113883i$$

$$x=\frac{\sqrt{10}i}{2}\approx 1.58113883i$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

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

Divide both sides by -2.

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

The equation is now solved.

$$x=\frac{\sqrt{10}i}{2} x=-\frac{\sqrt{10}i}{2}$$

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.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-5\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-5\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-5\right)}}{2\left(-2\right)}$$

Multiply 8 times -5.

$$x=\frac{0±\sqrt{-40}}{2\left(-2\right)}$$

Take the square root of -40.

$$x=\frac{0±2\sqrt{10}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{10}i}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{10}i}{-4} when ± is plus.

$$x=-\frac{\sqrt{10}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{10}i}{-4} when ± is minus.

$$x=\frac{\sqrt{10}i}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{10}i}{2} x=\frac{\sqrt{10}i}{2}$$