Solve x=sqrt{-y}

$$x = \sqrt { - y }$$

Solve for y

$$y=-x^{2}$$

$$x\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{-y}=x$$

Square both sides of the equation.

$$-y=x^{2}$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x^{2} by -1.

$$y=-x^{2}$$

Solve for y (complex solution)

$$y=-x^{2}$$

$$arg(x)<\pi \text{ or }x=0$$

Solve for x

$$x=\sqrt{-y}$$

$$y\leq 0$$