SOLUTION: find a number such that nine added to two times the number is equal to the product of the number and the quantity of one added to the number

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Question 376033: find a number such that nine added to two times the number is equal to the product of the number and the quantity of one added to the number
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2x+9=x(x+1)
2x+9=x^2+x
x^2-x-9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%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=%28-1%29%5E2-4%2A1%2A-9=37.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+37+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+37+%29%29%2F2%5C1+=+3.54138126514911
x%5B2%5D+=+%28-%28-1%29-sqrt%28+37+%29%29%2F2%5C1+=+-2.54138126514911

Quadratic expression 1x%5E2%2B-1x%2B-9 can be factored:
1x%5E2%2B-1x%2B-9+=+1%28x-3.54138126514911%29%2A%28x--2.54138126514911%29
Again, the answer is: 3.54138126514911, -2.54138126514911. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-9+%29

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Ed