Solve x=-sqrt{y+1}

$$x = - \sqrt { y + 1 }$$

Solve for y

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

$$x\leq 0$$

Steps for Solving Radical Equations

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

$$-\sqrt{y+1}=x$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x by -1.

$$\sqrt{y+1}=-x$$

Square both sides of the equation.

$$y+1=x^{2}$$

Subtract 1 from both sides of the equation.

$$y+1-1=x^{2}-1$$

Subtracting 1 from itself leaves 0.

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

Solve for y (complex solution)

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

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

Solve for x

$$x=-\sqrt{y+1}$$

$$y\geq -1$$