Solve (y+9)^2=(y-4)^2

$$( y + 9 ) ^ { 2 } = ( y - 4 ) ^ { 2 }$$

Solve for y

$$y = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

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

$$y^{2}+18y+81=\left(y-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-4\right)^{2}.

$$y^{2}+18y+81=y^{2}-8y+16$$

Subtract y^{2} from both sides.

$$y^{2}+18y+81-y^{2}=-8y+16$$

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

$$18y+81=-8y+16$$

Add 8y to both sides.

$$18y+81+8y=16$$

Combine 18y and 8y to get 26y.

$$26y+81=16$$

Subtract 81 from both sides.

$$26y=16-81$$

Subtract 81 from 16 to get -65.

$$26y=-65$$

Divide both sides by 26.

$$y=\frac{-65}{26}$$

Reduce the fraction \frac{-65}{26} to lowest terms by extracting and canceling out 13.

$$y=-\frac{5}{2}$$