Solve q_2^2+18+2=0

$$q _ { 2 } ^ { 2 } + 18 + 2 = 0$$

Solve for q_2

$$q_{2}=-2\sqrt{5}i\approx -0-4.472135955i$$

$$q_{2}=2\sqrt{5}i\approx 4.472135955i$$

Steps by Finding Square Root

Add 18 and 2 to get 20.

$$q_{2}^{2}+20=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$q_{2}^{2}=-20$$

The equation is now solved.

$$q_{2}=2\sqrt{5}i q_{2}=-2\sqrt{5}i$$

Steps Using the Quadratic Formula

Add 18 and 2 to get 20.

$$q_{2}^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q_{2}=\frac{0±\sqrt{0^{2}-4\times 20}}{2}$$

Square 0.

$$q_{2}=\frac{0±\sqrt{-4\times 20}}{2}$$

Multiply -4 times 20.

$$q_{2}=\frac{0±\sqrt{-80}}{2}$$

Take the square root of -80.

$$q_{2}=\frac{0±4\sqrt{5}i}{2}$$

Now solve the equation q_{2}=\frac{0±4\sqrt{5}i}{2} when ± is plus.

$$q_{2}=2\sqrt{5}i$$

Now solve the equation q_{2}=\frac{0±4\sqrt{5}i}{2} when ± is minus.

$$q_{2}=-2\sqrt{5}i$$

The equation is now solved.

$$q_{2}=2\sqrt{5}i q_{2}=-2\sqrt{5}i$$