Solve y=sqrt{4x-8}

$$y= \sqrt{ 4x-8 }$$

Solve for x

$$x=\frac{y^{2}+8}{4}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{4x-8}=y$$

Square both sides of the equation.

$$4x-8=y^{2}$$

Add 8 to both sides of the equation.

$$4x-8-\left(-8\right)=y^{2}-\left(-8\right)$$

Subtracting -8 from itself leaves 0.

$$4x=y^{2}-\left(-8\right)$$

Subtract -8 from y^{2}.

$$4x=y^{2}+8$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{y^{2}+8}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{y^{2}+8}{4}$$

Divide y^{2}+8 by 4.

$$x=\frac{y^{2}}{4}+2$$

Solve for x (complex solution)

$$x=\frac{y^{2}+8}{4}$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 2$$