Question 205643
1) {{{L = 2W+5}}} "The length (L) of a rectangle is 5 more than twice its width (W)."
2) {{{L*W = 102}}}sq.in. "The area of the rectangle is 102 inches square."
What is L? 
Substitute the L from equation 1) into equation 2) and solve for W.
{{{(2W+5)*W = 102}}}
{{{2W^2+5W = 102}}} Subtract 102 from both sides.
{{{2W^2+5W-102 = 0}}} Factor this quadratic equation.
{{{(2W+17)(W-6) = 0}}} Apply the zero product rule.
{{{2W+17 = 0}}} or {{{W-6 = 0}}} which means that...
{{{2W = -17}}} or {{{W = 6}}} Discard the negative solution as the width, W, must be a positive value.
{{{W = 6}}}inches and...
{{{L = 2W+5}}}
{{{L = 2(6)+5}}}
{{{highlight(L = 17)}}}inches.