SOLUTION: Can someone help me solve this please? w^4-18w^2-2=0 What is the solution?

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Question 332342: Can someone help me solve this please?
w^4-18w^2-2=0
What is the solution?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's a quadratic in w^2
Sub x for w^2 and solve it with the quadratic eqn.
Then, each of the 2 solutions = w^2
Take the sq root of each of them.
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Solve for x, which is w^2
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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w^2 = 9 ± sqrt(83)
w+=+sqrt%289+%2B+sqrt%2883%29%29 =~ 18.1104
w+=+sqrt%289+-+sqrt%2883%29%29 =~ 0.1104
w+=+-sqrt%289+%2B+sqrt%2883%29%29 =~ -18.1104
w+=+-sqrt%289+-+sqrt%2883%29%29 =~ -0.1104