Solve -x(x+2)=-sqrt{y}

$$-x(x+2)=- \sqrt{ y }$$

Solve for y

$$y=\left(x\left(x+2\right)\right)^{2}$$

$$x\leq -2\text{ or }x\geq 0$$

Steps for Solving Radical Equations

Use the distributive property to multiply -x by x+2.

$$\left(-x\right)x+2\left(-x\right)=-\sqrt{y}$$

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

$$-\sqrt{y}=\left(-x\right)x+2\left(-x\right)$$

Multiply x and x to get x^{2}.

$$-\sqrt{y}=-x^{2}+2\left(-1\right)x$$

Multiply 2 and -1 to get -2.

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

Divide both sides by -1.

$$\frac{-\sqrt{y}}{-1}=-\frac{x\left(x+2\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{y}=-\frac{x\left(x+2\right)}{-1}$$

Divide -x\left(2+x\right) by -1.

$$\sqrt{y}=x\left(x+2\right)$$

Square both sides of the equation.

$$y=x^{2}\left(x+2\right)^{2}$$

Solve for x (complex solution)

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

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

Solve for y (complex solution)

$$y=\left(x\left(x+2\right)\right)^{2}$$

$$arg(x\left(x+2\right))<\pi \text{ or }x=-2\text{ or }x=0$$

Solve for x

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

$$x=-\sqrt{\sqrt{y}+1}-1\text{, }y\geq 0$$