SOLUTION: how do i convert this into a form i can solve as a quadratic equation? 9(p-300)^2= 1.02^2 *p(400-p)

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Question 173108: how do i convert this into a form i can solve as a quadratic equation?
9(p-300)^2= 1.02^2 *p(400-p)
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
how do i convert this into a form i can solve as a quadratic equation?
9(p-300)^2= 1.02^2 *p(400-p)
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expand all the terms.
9(p-300)^2= 1.02^2 *p(400-p)
9(p^2 - 600p + 90000) = 1.0404*(400p - p^2)
9p^2 - 5400 p + 810000 = 416.16p - 1.0404p^2
p^2 - 600p + 90000 = 46.24p - 0.1156p^2
Collect terms
1.1156p^2 - 646.24p + 90000 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=16010.1376 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 346.34778255817, 232.92794350852. Here's your graph: