Solve y-10=(x+1)^2

$$y - 10 = ( x + 1 ) ^ { 2 }$$

Solve for y

$$y=\left(x+1\right)^{2}+10$$

Solution Steps

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

$$y-10=x^{2}+2x+1$$

Add 10 to both sides.

$$y=x^{2}+2x+1+10$$

Add 1 and 10 to get 11.

$$y=x^{2}+2x+11$$

Solve for x (complex solution)

$$x=-\left(\sqrt{y-10}+1\right)$$

$$x=\sqrt{y-10}-1$$

Solve for x

$$x=-\left(\sqrt{y-10}+1\right)$$

$$x=\sqrt{y-10}-1\text{, }y\geq 10$$