Question 916965
Let w be the uniform width of uncovered floor.

Rug area is {{{(14-2w)(15-2w)}}}
Rug area is also given as 110 square feet.


{{{(14-2w)(15-2w)=110}}}, equality of the two area numbers
{{{2*(7-w)(15-2w)=55*2}}}
{{{(7-w)(15-2w)=55}}}
{{{105-15w-14w+2w^2=55}}}
{{{50-29w+2w^2=0}}}
{{{highlight_green(2w^2-29w+50=0)}}}


You can try to factor that, or just use general formula for solution of quadratic equation.


{{{w=(29+- sqrt(29^2-4*2*50))/(2*2)}}}
{{{w=(29+- sqrt(441))/(2*2)}}}
{{{w=(29+- 21)/4}}}---- Only one of which should make sense.


{{{cross(w=12.5)}}}  or  {{{highlight(w=2)}}}