Solve x=-(y+8)^2

$$x = - ( y + 8 ) ^ { 2 }$$

Solve for x

$$x=-\left(y+8\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+8\right)^{2}.

$$x=-\left(y^{2}+16y+64\right)$$

To find the opposite of y^{2}+16y+64, find the opposite of each term.

$$x=-y^{2}-16y-64$$

Solve for y (complex solution)

$$y=-i\sqrt{x}-8$$

$$y=i\sqrt{x}-8$$

Solve for y

$$y=-\left(\sqrt{-x}+8\right)$$

$$y=\sqrt{-x}-8\text{, }x\leq 0$$