Solve y=-sqrt{2x+1}

$$y = - \sqrt { 2 x + 1 }$$

Solve for x

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

$$y\leq 0$$

Steps for Solving Radical Equations

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

$$-\sqrt{2x+1}=y$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide y by -1.

$$\sqrt{2x+1}=-y$$

Square both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for x (complex solution)

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

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

Solve for y

$$y=-\sqrt{2x+1}$$

$$x\geq -\frac{1}{2}$$