Solve x^2-12x-6xi+c=0

$$x ^ { 2 } - 12 x - 6 x i + c = 0$$

Solve for c

$$c=6\xi +12x-x^{2}$$

Solution Steps

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

$$-12x-6\xi +c=-x^{2}$$

Add 12x to both sides.

$$-6\xi +c=-x^{2}+12x$$

Add 6\xi to both sides.

$$c=-x^{2}+12x+6\xi$$

Solve for x (complex solution)

$$x=\sqrt{36+6\xi -c}+6$$

$$x=-\sqrt{36+6\xi -c}+6$$

Solve for x

$$x=\sqrt{36+6\xi -c}+6$$

$$x=-\sqrt{36+6\xi -c}+6\text{, }\xi \geq \frac{c}{6}-6$$