SOLUTION: I've been stuck on this problem for a really long time. I'm trying to figure out a problem reducible to a quadratic equation in a step by step method so I can understand how I get

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Question 370127: I've been stuck on this problem for a really long time. I'm trying to figure out a problem reducible to a quadratic equation in a step by step method so I can understand how I get from one point to the other.
The problem is: w^4-6w^2-2=0
I only know this:
u = w^2
From my text and all the research I've done, I also know that I would rewrite this problem as:

u^2 - 6u - 2 = 0
I have to solve this but it's not factorable which is where I am absolutely stumped. This is an example problem on my homework I'm providing here so I have the answers for that but I just don't know how they got them.
This is the way they worked it out.....
u^2-6u-2=0
they solve for u...but how????
they got the answer
u=3-sqrt11 or u=3+sqrt11
then after this the problem needs to be solved for w.
Is there any way you can help and show me in a step by step fashion so I get this? Thank you. LeAnn
Found 2 solutions by jim_thompson5910, ewatrrr:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
You found that or , which is completely correct. However, we want to solve for 'w'.

Recall that you let .


So plug this into the two equations above to get


or


Now we need to solve each equation for 'w'. We'll do this by taking the square root of both sides.


So solve for w to get


or



Now solve for w to get


or


So the four solutions are



, , , or


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi,

w^4 - 6u^2 - 2 = 0 

using the Pythagorean Theorem to solve for w^2









w^2 = 3 + 3.317 = 6.317

w = 2.512

w = -2.513

w^2 = 3 - 3.317 = -.317

w = .563*i

w = -.563*i 

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