Solve x+left(y+6right)^2=9

$$x+ { \left(y+6 \right) }^{ 2 } = 9$$

Solve for x

$$x=-\left(y+3\right)\left(y+9\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+6\right)^{2}.

$$x+y^{2}+12y+36=9$$

Subtract y^{2} from both sides.

$$x+12y+36=9-y^{2}$$

Subtract 12y from both sides.

$$x+36=9-y^{2}-12y$$

Subtract 36 from both sides.

$$x=9-y^{2}-12y-36$$

Subtract 36 from 9 to get -27.

$$x=-27-y^{2}-12y$$

Solve for y (complex solution)

$$y=-\left(\sqrt{9-x}+6\right)$$

$$y=\sqrt{9-x}-6$$

Solve for y

$$y=-\left(\sqrt{9-x}+6\right)$$

$$y=\sqrt{9-x}-6\text{, }x\leq 9$$