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

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

Solve for y

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+9\right)^{2}.

$$x^{2}+18x+81=y$$

Swap sides so that all variable terms are on the left hand side.

$$y=x^{2}+18x+81$$

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\sqrt{y}-9\text{, }y\geq 0$$