Solve y=sqrt{x+1-3}

$$y= \sqrt{ x+1-3 }$$

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

Subtract 3 from 1 to get -2.

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

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

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

Square both sides of the equation.

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

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from y^{2}.

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

Solve for x (complex solution)

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

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 2$$