Solve y=-0.5sqrt{-x}

$$y=-0.5 \sqrt{ -x }$$

Solve for x

$$x=-4y^{2}$$

$$y\leq 0$$

Steps for Solving Radical Equations

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

$$-0.5\sqrt{-x}=y$$

Multiply both sides by -2.

$$\frac{-0.5\sqrt{-x}}{-0.5}=\frac{y}{-0.5}$$

Dividing by -0.5 undoes the multiplication by -0.5.

$$\sqrt{-x}=\frac{y}{-0.5}$$

Divide y by -0.5 by multiplying y by the reciprocal of -0.5.

$$\sqrt{-x}=-2y$$

Square both sides of the equation.

$$-x=4y^{2}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{4y^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{4y^{2}}{-1}$$

Divide 4y^{2} by -1.

$$x=-4y^{2}$$

Solve for x (complex solution)

$$x=-4y^{2}$$

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

Solve for y (complex solution)

$$y=-\frac{\sqrt{-x}}{2}$$

Solve for y

$$y=-\frac{\sqrt{-x}}{2}$$

$$x\leq 0$$