Solve x^2+4=-4

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

Solve for x (complex solution)

$$x=-2\sqrt{2}i\approx -0-2.828427125i$$

$$x=2\sqrt{2}i\approx 2.828427125i$$

Steps by Finding Square Root

Subtract 4 from both sides.

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

Subtract 4 from -4 to get -8.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Add 4 to both sides.

$$x^{2}+4+4=0$$

Add 4 and 4 to get 8.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8}}{2}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32}}{2}$$

Take the square root of -32.

$$x=\frac{0±4\sqrt{2}i}{2}$$

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

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

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

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

The equation is now solved.

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