SOLUTION: The square of number, increased by 12, is the same as the product of seven and the number, find the numbers.

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Question 446261: The square of number, increased by 12, is the same as the product of seven and the number, find the numbers.
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number.
x%5E2%2B12=7x
x%5E2-7x%2B12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B12+=+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=%28-7%29%5E2-4%2A1%2A12=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-7%29-sqrt%28+1+%29%29%2F2%5C1+=+3

Quadratic expression 1x%5E2%2B-7x%2B12 can be factored:
1x%5E2%2B-7x%2B12+=+1%28x-4%29%2A%28x-3%29
Again, the answer is: 4, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B12+%29

The number is 3 or 4.