Solve x^2+9=-18

$$x ^ { 2 } + 9 = - 18$$

Solve for x (complex solution)

$$x=-3\sqrt{3}i\approx -0-5.196152423i$$

$$x=3\sqrt{3}i\approx 5.196152423i$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$x^{2}=-18-9$$

Subtract 9 from -18 to get -27.

$$x^{2}=-27$$

The equation is now solved.

$$x=3\sqrt{3}i x=-3\sqrt{3}i$$

Steps Using the Quadratic Formula

Add 18 to both sides.

$$x^{2}+9+18=0$$

Add 9 and 18 to get 27.

$$x^{2}+27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 27}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 27}}{2}$$

Multiply -4 times 27.

$$x=\frac{0±\sqrt{-108}}{2}$$

Take the square root of -108.

$$x=\frac{0±6\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±6\sqrt{3}i}{2} when ± is plus.

$$x=3\sqrt{3}i$$

Now solve the equation x=\frac{0±6\sqrt{3}i}{2} when ± is minus.

$$x=-3\sqrt{3}i$$

The equation is now solved.

$$x=3\sqrt{3}i x=-3\sqrt{3}i$$