SOLUTION: Solve for "P": 2P^2-2P-5=0

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Question 169326: Solve for "P": 2P^2-2P-5=0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2P^2-2P-5=0
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Always try to factor first, failing that you can always use the "quadratic equation". In this case, you can't factor so you must use the quadratic equation.
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Doing so will yield:
P = {2.158, -1.158}
.
Details of the quadratic below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aP%5E2%2BbP%2Bc=0 (in our case 2P%5E2%2B-2P%2B-5+=+0) has the following solutons:

P%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=%28-2%29%5E2-4%2A2%2A-5=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+44+%29%29%2F2%5Ca.

P%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+44+%29%29%2F2%5C2+=+2.1583123951777
P%5B2%5D+=+%28-%28-2%29-sqrt%28+44+%29%29%2F2%5C2+=+-1.1583123951777

Quadratic expression 2P%5E2%2B-2P%2B-5 can be factored:
2P%5E2%2B-2P%2B-5+=+2%28P-2.1583123951777%29%2A%28P--1.1583123951777%29
Again, the answer is: 2.1583123951777, -1.1583123951777. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-2%2Ax%2B-5+%29