SOLUTION: find all solutions x^3-512=0

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Question 661465: find all solutions
x^3-512=0

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find all solutions
x^3-512=0
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%28x-8%29%2A%28x%5E2+%2B+8x+%2B+64%29+=+0
x = 8
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%28x%5E2+%2B+8x+%2B+64%29+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B64+=+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=%288%29%5E2-4%2A1%2A64=-192.

The discriminant -192 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 -192 is + or - sqrt%28+192%29+=+13.856406460551.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B64+%29

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x+=+-4+%2B+4sqrt%283%29
x+=+-4+-+4sqrt%283%29