SOLUTION: A square has all its edge lenghts increased by 3cm. This makes a new square with twice the area of the old one. What was the area of the old square. i was wondering if you c

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Question 267551: A square has all its edge lenghts increased by 3cm.
This makes a new square with twice the area of the old one.
What was the area of the old square.
i was wondering if you could show me how this is worked out
it is to help my daughter for school thanks Valerie
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A square has all its edge lenghts increased by 3cm.
This makes a new square with twice the area of the old one.
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Call the original side length s
The original area is s^2.
(s+3)*(s+3) = 2s^2
s^2 + 6s + 9 = 2s^2
s^2 - 6s - 9 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-9+=+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=%28-6%29%5E2-4%2A1%2A-9=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+7.24264068711928
x%5B2%5D+=+%28-%28-6%29-sqrt%28+72+%29%29%2F2%5C1+=+-1.24264068711928

Quadratic expression 1x%5E2%2B-6x%2B-9 can be factored:
1x%5E2%2B-6x%2B-9+=+%28x-7.24264068711928%29%2A%28x--1.24264068711928%29
Again, the answer is: 7.24264068711928, -1.24264068711928. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-9+%29

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Ignore the negative answer
s+=+3+%2B+3sqrt%282%29 cm
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It's probably messier than you expected.