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

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

Solve for y

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

Solution Steps

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

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\sqrt{-y}-1\text{, }y\leq 0$$