SOLUTION: I have the horrible problem that I am having a very hard time with, please help The problem is solve for x: w^4-18w^2-2=0 Thanks a lot

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Question 460191: I have the horrible problem that I am having a very hard time with, please help
The problem is solve for x: w^4-18w^2-2=0
Thanks a lot
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
w%5E4-18w%5E2-2=0
Sub x for w^2
x%5E2+-+18x+-+2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-18x%2B-2+=+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=%28-18%29%5E2-4%2A1%2A-2=332.

Discriminant d=332 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+332+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+332+%29%29%2F2%5C1+=+18.1104335791443
x%5B2%5D+=+%28-%28-18%29-sqrt%28+332+%29%29%2F2%5C1+=+-0.110433579144299

Quadratic expression 1x%5E2%2B-18x%2B-2 can be factored:
1x%5E2%2B-18x%2B-2+=+%28x-18.1104335791443%29%2A%28x--0.110433579144299%29
Again, the answer is: 18.1104335791443, -0.110433579144299. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B-2+%29

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Sub back.
w^2 = 9 + sqrt(58)
w = +4.076
w = -4.076
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w^2 = 9 - sqrt(58)
w = =1.7615
w = -1.1765