SOLUTION: A rectangular instrument case has an are of 40in^2. if the length is 6in. more than the width, find the dimensions of the length. (A=L*W)

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Question 248260: A rectangular instrument case has an are of 40in^2. if the length is 6in. more than the width, find the dimensions of the length. (A=L*W)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
40=L*W
L=6+W
substitute 6+w for L in 40=L*W to get 40=(6+W)*W
40=(6+W)*W
40=6W+W^2
subtract 40 from both sides and move everything to the opposite sides
W^2+6W-40=0
to factor we need factors of 40 that are different by 6
factors of 40
40*1;20*2;10*4;5*8
which ones are different by 6
10 and 4
we need positive six so we need 10-4
(x-4)(x+10)=0
x=4 and x=-10
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-40+=+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=%286%29%5E2-4%2A1%2A-40=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%286%29-sqrt%28+196+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B6x%2B-40 can be factored:
1x%5E2%2B6x%2B-40+=+1%28x-4%29%2A%28x--10%29
Again, the answer is: 4, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-40+%29