SOLUTION: mr.jackson has a rectangular garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden

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Question 936234: mr.jackson has a rectangular garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let width be x feet
length was 4 less than twice the width
length = 2*x-4
area = width x length
420 = x* (2x-4)
420 = x*2x-x*4
+420+=2x%5E2-4x
move 420 to the right
0+=+2x%5E2-4x-420
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-4x%2B-420+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A2%2A-420=3376.

Discriminant d=3376 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+3376+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+3376+%29%29%2F2%5C2+=+15.5258390463339
x%5B2%5D+=+%28-%28-4%29-sqrt%28+3376+%29%29%2F2%5C2+=+-13.5258390463339

Quadratic expression 2x%5E2%2B-4x%2B-420 can be factored:
2x%5E2%2B-4x%2B-420+=+2%28x-15.5258390463339%29%2A%28x--13.5258390463339%29
Again, the answer is: 15.5258390463339, -13.5258390463339. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B-420+%29

x= 15.53 , -13.53
but x cannot be negative
hence width (w) = 15.53 feet
length (l) = 2*15.53-4
= 31.06-4
= 27.06 feet
length = 27.06 feet & width = 15.53 feet