Solve x^2+8=-x^2-8?

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

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Subtract 8 from both sides.

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

Subtract 8 from -8 to get -16.

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

Divide both sides by 2.

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

Divide -16 by 2 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 x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Add 8 to both sides.

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

Add 8 and 8 to get 16.

$$2x^{2}+16=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 16}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 16}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 16}}{2\times 2}$$

Multiply -8 times 16.

$$x=\frac{0±\sqrt{-128}}{2\times 2}$$

Take the square root of -128.

$$x=\frac{0±8\sqrt{2}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{2}i}{4}$$

Now solve the equation x=\frac{0±8\sqrt{2}i}{4} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{2}i}{4} when ± is minus.

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

The equation is now solved.

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