SOLUTION: Solve: 125x^3-27=0

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Question 580692: Solve: 125x^3-27=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve: 125x^3-27=0
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%285x-3%29%2A%2825x%5E2+%2B+15x+%2B+9%29+=+0
5x-3 = 0
x = 3/5
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%2825x%5E2+%2B+15x+%2B+9%29+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B15x%2B9+=+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=%2815%29%5E2-4%2A25%2A9=-675.

The discriminant -675 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -675 is + or - sqrt%28+675%29+=+25.9807621135332.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B15%2Ax%2B9+%29

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