Question 994251
{{{system(u=unknownWidth,L=120,w=80)}}}


Factory area,  wL
Combined Factory & Lawn area, (w+2u)(L+2u)
Lawn area requirement, {{{highlight_green((L+2u)(w+2u)-wL=wL)}}}


Simplify that equation and solve for u.


{{{wL+2wu+2Lu+4u^2-wL=wL}}}
{{{(2w+2L)u+4u^2=wL}}}
{{{highlight_green(4u^2+(2w+2L)u-wL=0)}}}


Substitute whenever you are ready, but solve for u.  Formula for general solution of quadratic equation can be used.


{{{u=(-(2w+2L)+sqrt((2w+2L)^2-4*4*(-wL)))/(2*4)}}}
{{{u=(-2w-2L+sqrt(4w^2+8wL+4L^2+4*4*wL))/(2*4)}}}
{{{u=(-2w-2L+2*sqrt(w^2+4wL+L^2+4wL))/(2*4)}}}
{{{highlight(u=(-w-L+sqrt(w^2+8wL+L^2))/4)}}}



---
The PLUS form is needed in the formula for quadratic equation because we must have a positive value for u.  w and L are both positive, but they are used as SUBTRACTED in the numerator of the formula of quadratic equation solution.


Most of the time, students would want to substitute the given values just after finding the quadratic equation in the green rectangular outline shown  (IF they are starting the problem solution and analysis in symbolic form as done in this example).