SOLUTION: SOLVE 25x^3-15x^2=18x

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Question 167675: SOLVE
25x^3-15x^2=18x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
25x^3-15x^2=18x
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25x%5E3+-+15x%5E2+-+18x+=+0
Divide by x, so x = 0 is one solution.
25x%5E2+-+15x+-+18+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B-15x%2B-18+=+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=%28-15%29%5E2-4%2A25%2A-18=2025.

Discriminant d=2025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+2025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+2025+%29%29%2F2%5C25+=+1.2
x%5B2%5D+=+%28-%28-15%29-sqrt%28+2025+%29%29%2F2%5C25+=+-0.6

Quadratic expression 25x%5E2%2B-15x%2B-18 can be factored:
25x%5E2%2B-15x%2B-18+=+%28x-1.2%29%2A%28x--0.6%29
Again, the answer is: 1.2, -0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B-15%2Ax%2B-18+%29

The solutions are correct, but the factors are not.
25x%5E3+-+15x%5E2+-+18x+=+0
x%2A%285x-6%29%2A%285x%2B3%29+=+0
x = 0, 1.2, -0.6