Solve y=-sqrt{2x-5}

$$y = - \sqrt { 2 x - 5 }$$

Solve for x

$$x=\frac{y^{2}+5}{2}$$

$$y\leq 0$$

Steps for Solving Radical Equations

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

$$-\sqrt{2x-5}=y$$

Divide both sides by -1.

$$\frac{-\sqrt{2x-5}}{-1}=\frac{y}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{2x-5}=\frac{y}{-1}$$

Divide y by -1.

$$\sqrt{2x-5}=-y$$

Square both sides of the equation.

$$2x-5=y^{2}$$

Add 5 to both sides of the equation.

$$2x-5-\left(-5\right)=y^{2}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$2x=y^{2}-\left(-5\right)$$

Subtract -5 from y^{2}.

$$2x=y^{2}+5$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{2}+5}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{2}+5}{2}$$

Solve for x (complex solution)

$$x=\frac{y^{2}+5}{2}$$

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

Solve for y

$$y=-\sqrt{2x-5}$$

$$x\geq \frac{5}{2}$$