SOLUTION: Twice the square of a positive integer is 35 more than 9 times that integer. What is the integer?

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Question 73069: Twice the square of a positive integer is 35 more than 9 times that integer. What is the integer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember "is" means equals.
2%28x%29%5E2=35%2B9xHere's the translated version
2x%5E2-9x-35=0Solve for x by getting everything to one side
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-9x%2B-35+=+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=%28-9%29%5E2-4%2A2%2A-35=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+361+%29%29%2F2%5C2+=+7
x%5B2%5D+=+%28-%28-9%29-sqrt%28+361+%29%29%2F2%5C2+=+-2.5

Quadratic expression 2x%5E2%2B-9x%2B-35 can be factored:
2x%5E2%2B-9x%2B-35+=+2%28x-7%29%2A%28x--2.5%29
Again, the answer is: 7, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-9%2Ax%2B-35+%29

Since the problem states the integer is positive, the only answer is 7. So 7 is the integer.
Check:
2%287%29%5E2=35%2B9%287%29
98=98Works