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

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

Solve for y

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

Solution Steps

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

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

Add 1 and 1 to get 2.

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

Solve for x (complex solution)

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

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

Solve for x

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

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