Question 716557
Total Area minus pool area gives border area.

{{{(110+2x)(40+2x)-(110)(40)}}}= Border Area.  That simplifies depending on how far you take it, to Border Area ={{{ 4(x+55)(x+20)-4400}}}.  Note that the pool "area" alone is {{{110*40}}} sq.ft.


Finding how wide the border if the area must be 936 sq.ft., why would we not use quadratic formula?  If we begin with {{{936=4(x+55)(x+20)-4400}}}, when we carry through the steps, ... we obtain without any trouble, the much simpler and good equation of ...

{{{highlight(x^2+75-234=0)}}}.  


That does not appear factorable.  Why should we use something other than quadratic formula?  THE TRICK IS TO FACTOR 234.


{{{234=2*3*3*13}}}, and 3 and 2*3*13 are the same as 3 and 78.
The quadratic equation could be factored into:
{{{highlight((x+78)(x-3)=0)}}}. 


The reasonable answer finally is 3 feet width.  x=3.