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

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) (Show Source): You can put this solution on YOUR website!

Sub x for w^2

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=332 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 18.1104335791443, -0.110433579144299. Here's your graph:

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

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