Solve q_1^2+q+1/4=0

$$q _ { 1 } ^ { 2 } + q + \frac { 1 } { 4 } = 0$$

Solve for q

$$q=-q_{1}^{2}-\frac{1}{4}$$

Solution Steps

Subtract q_{1}^{2} from both sides. Anything subtracted from zero gives its negation.

$$q+\frac{1}{4}=-q_{1}^{2}$$

Subtract \frac{1}{4} from both sides.

$$q=-q_{1}^{2}-\frac{1}{4}$$

Solve for q_1 (complex solution)

$$q_{1}=-\frac{\sqrt{-4q-1}}{2}$$

$$q_{1}=\frac{\sqrt{-4q-1}}{2}$$

Solve for q_1

$$q_{1}=\frac{\sqrt{-4q-1}}{2}$$

$$q_{1}=-\frac{\sqrt{-4q-1}}{2}\text{, }q\leq -\frac{1}{4}$$