Solve left(y+1right)^2=y^2+9

$${ \left(y+1 \right) }^{ 2 } = { y }^{ 2 } +9$$

Solve for y

$$y=4$$

Steps for Solving Linear Equation

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

$$y^{2}+2y+1=y^{2}+9$$

Subtract y^{2} from both sides.

$$y^{2}+2y+1-y^{2}=9$$

Combine y^{2} and -y^{2} to get 0.

$$2y+1=9$$

Subtract 1 from both sides.

$$2y=9-1$$

Subtract 1 from 9 to get 8.

$$2y=8$$

Divide both sides by 2.

$$y=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$y=4$$