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) About Me  (Show Source):
You can put this solution on YOUR website!
You found that u=3-sqrt%2811%29 or u=3%2Bsqrt%2811%29, which is completely correct. However, we want to solve for 'w'.

Recall that you let u=w%5E2.


So plug this into the two equations above to get


w%5E2=3-sqrt%2811%29 or w%5E2=3%2Bsqrt%2811%29


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


So solve w%5E2=3-sqrt%2811%29 for w to get


w=sqrt%283-sqrt%2811%29%29 or w=-sqrt%283-sqrt%2811%29%29



Now solve w%5E2=3%2Bsqrt%2811%29 for w to get


w=sqrt%283%2Bsqrt%2811%29%29 or w=-sqrt%283%2Bsqrt%2811%29%29


So the four solutions are



w=sqrt%283-sqrt%2811%29%29, w=-sqrt%283-sqrt%2811%29%29, w=sqrt%283%2Bsqrt%2811%29%29, or w=-sqrt%283%2Bsqrt%2811%29%29


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) About Me  (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%5E2+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

w%5E2+=+%286+%2B-+sqrt%28+44+%29%29%2F%282%29+

w%5E2+=+%286+%2B-+2%2Asqrt%2811%29%29%2F%282%29+

w%5E2+=+%283%2B-+sqrt%2811%29%29

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