Solve sqrt{2x-1}+|y-1|=0

$$\sqrt { 2 x - 1 } + | y - 1 | = 0$$

Solve for x

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

$$y-1\geq 0\text{ and }y\leq 1$$

Steps for Solving Radical Equations

Subtract |y-1| from both sides of the equation.

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

Subtracting |y-1| from itself leaves 0.

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

Square both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

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

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for y

$$y=1$$

$$x = \frac{1}{2} = 0.5$$