Solve y=1+sqrt{x-1}

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

Solve for x

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

$$-\left(1-y\right)\geq 0$$

Steps for Solving Radical Equations

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

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

Subtract 1 from both sides.

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

Square both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from \left(y-1\right)^{2}.

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

Solve for x (complex solution)

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

$$y=1\text{ or }arg(1-y)\geq \pi$$

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 1$$