Solve y^2+1=(4-y)^2

$$y ^ { 2 } + 1 = ( 4 - y ) ^ { 2 }$$

Solve for y

$$y = \frac{15}{8} = 1\frac{7}{8} = 1.875$$

Steps for Solving Linear Equation

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

$$y^{2}+1=16-8y+y^{2}$$

Add 8y to both sides.

$$y^{2}+1+8y=16+y^{2}$$

Subtract y^{2} from both sides.

$$y^{2}+1+8y-y^{2}=16$$

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

$$1+8y=16$$

Subtract 1 from both sides.

$$8y=16-1$$

Subtract 1 from 16 to get 15.

$$8y=15$$

Divide both sides by 8.

$$y=\frac{15}{8}$$