Solve -1/y=x^2+c

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

Solve for c

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

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$-1=yx^{2}+yc$$

Swap sides so that all variable terms are on the left hand side.

$$yx^{2}+yc=-1$$

Subtract yx^{2} from both sides.

$$yc=-1-yx^{2}$$

Reorder the terms.

$$cy=-yx^{2}-1$$

The equation is in standard form.

$$yc=-yx^{2}-1$$

Divide both sides by y.

$$\frac{yc}{y}=\frac{-yx^{2}-1}{y}$$

Dividing by y undoes the multiplication by y.

$$c=\frac{-yx^{2}-1}{y}$$

Divide -1-yx^{2} by y.

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

Solve for x (complex solution)

$$x=-\sqrt{-c-\frac{1}{y}}$$

$$x=\sqrt{-c-\frac{1}{y}}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt{-c-\frac{1}{y}}$$

$$x=-\sqrt{-c-\frac{1}{y}}\text{, }\left(c\leq 0\text{ and }y<0\right)\text{ or }\left(y\geq -\frac{1}{c}\text{ and }c<0\text{ and }y\neq 0\right)\text{ or }\left(y\geq -\frac{1}{c}\text{ and }y<0\right)$$