Solve x^2+2=-8

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

Solve for x (complex solution)

$$x=-\sqrt{10}i\approx -0-3.16227766i$$

$$x=\sqrt{10}i\approx 3.16227766i$$

Steps by Finding Square Root

Subtract 2 from both sides.

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

Subtract 2 from -8 to get -10.

$$x^{2}=-10$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Add 8 to both sides.

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

Add 2 and 8 to get 10.

$$x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10}}{2}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40}}{2}$$

Take the square root of -40.

$$x=\frac{0±2\sqrt{10}i}{2}$$

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

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

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

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

The equation is now solved.

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