Solve y+1=(x-1)^2

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

Solve for y

$$y=x\left(x-2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Subtract 1 from both sides.

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

Subtract 1 from 1 to get 0.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\sqrt{y+1}+1\text{, }y\geq -1$$