Solve y=1/2sqrt{x-1}

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

Solve for x

$$x=4y^{2}+1$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

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

Multiply both sides by 2.

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

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

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

Divide y by \frac{1}{2} by multiplying y by the reciprocal of \frac{1}{2}.

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

Square both sides of the equation.

$$x-1=4y^{2}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=4y^{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=4y^{2}-\left(-1\right)$$

Subtract -1 from 4y^{2}.

$$x=4y^{2}+1$$

Solve for x (complex solution)

$$x=4y^{2}+1$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 1$$