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

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) (Show Source): You can put this solution on YOUR website!
Remember "is" means equals.
Here's the translated version
Solve for x by getting everything to one side

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=361 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -2.5. Here's your graph:

Since the problem states the integer is positive, the only answer is 7. So 7 is the integer.
Check:

Works
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