Question 131640
The length of a rectangular flower bed is 3 feet less than twice its width. The area of the bed is 54 sq. ft. Find the dimensions of the flower bed. 

ask your self what is the shape? rectangualr
 then ask what is the Area the rectangular= length * width = L.W
then what is the perimeter = 2 L + 2 w

L = 3-2W " Length is 3 less than twice the width " i translate it into math 
A= 54------> L.W=54 solve for L------> L= 54/w

sub this value in the first equation instead of L

L= 3-2w
54/w = 3-2w  multiply by W to get ridoff the fraction
54=3w-2w^2
collect then in one side
2w^2-3W+54=0
 factor this   {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
         
x= -(-3)+-sqrt((-3)^2-4(2)(54)) /2*(2) = 3+- sqrt(negative #)
CAN NOT BE FACTORED