SOLUTION: positive integer is 11 more than 28 times another. Their product is 11420. Find the two integers

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Question 964084: positive integer is 11 more than 28 times another. Their product is 11420. Find the two integers
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Set x = the larger number
y = the smaller number
x = 11 + 28y
x*y = 11420
substitute ( 11+28y ) for x
( 11+28y )y =11420
11y + 28y^2 = 11420
28y^2 + 11y - 11420 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 28x%5E2%2B11x%2B-11420+=+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=%2811%29%5E2-4%2A28%2A-11420=1279161.

Discriminant d=1279161 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+1279161+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+1279161+%29%29%2F2%5C28+=+20
x%5B2%5D+=+%28-%2811%29-sqrt%28+1279161+%29%29%2F2%5C28+=+-20.3928571428571

Quadratic expression 28x%5E2%2B11x%2B-11420 can be factored:
28x%5E2%2B11x%2B-11420+=+28%28x-20%29%2A%28x--20.3928571428571%29
Again, the answer is: 20, -20.3928571428571. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+28%2Ax%5E2%2B11%2Ax%2B-11420+%29

Based upon solver solution above, y = 20
Since x*y = 11420,
x = 11420/20
x = 571