Solve x^2+y^2-6x-8y-c=0

$$x ^ { 2 } + y ^ { 2 } - 6 x - 8 y - c = 0$$

Solve for c

$$c=x^{2}-6x+y^{2}-8y$$

Steps for Solving Linear Equation

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

$$y^{2}-6x-8y-c=-x^{2}$$

Subtract y^{2} from both sides.

$$-6x-8y-c=-x^{2}-y^{2}$$

Add 6x to both sides.

$$-8y-c=-x^{2}-y^{2}+6x$$

Add 8y to both sides.

$$-c=-x^{2}-y^{2}+6x+8y$$

The equation is in standard form.

$$-c=8y-y^{2}+6x-x^{2}$$

Divide both sides by -1.

$$\frac{-c}{-1}=\frac{8y-y^{2}+6x-x^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$c=\frac{8y-y^{2}+6x-x^{2}}{-1}$$

Divide -x^{2}-y^{2}+6x+8y by -1.

$$c=x^{2}-6x+y^{2}-8y$$

Solve for x (complex solution)

$$x=\sqrt{9+c+8y-y^{2}}+3$$

$$x=-\sqrt{9+c+8y-y^{2}}+3$$

Solve for x

$$x=\sqrt{9+c+8y-y^{2}}+3$$

$$x=-\sqrt{9+c+8y-y^{2}}+3\text{, }c\geq -\left(9+8y-y^{2}\right)$$