Solve -4x^2-16=0

$$- 4 x ^ { 2 } - 16 = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Add 16 to both sides. Anything plus zero gives itself.

$$-4x^{2}=16$$

Divide both sides by -4.

$$x^{2}=\frac{16}{-4}$$

Divide 16 by -4 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.

$$-4x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\left(-16\right)}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\left(-16\right)}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\left(-16\right)}}{2\left(-4\right)}$$

Multiply 16 times -16.

$$x=\frac{0±\sqrt{-256}}{2\left(-4\right)}$$

Take the square root of -256.

$$x=\frac{0±16i}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±16i}{-8}$$

Now solve the equation x=\frac{0±16i}{-8} when ± is plus.

$$x=-2i$$

Now solve the equation x=\frac{0±16i}{-8} when ± is minus.

$$x=2i$$

The equation is now solved.

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