SOLUTION: I am having such a time understanding how to solve... w^4 - 20w^2 - 2 = 0. It is not qudratic but is to be reduced to a quadratic equation in order for us to solve it. It is said

Question 128015: I am having such a time understanding how to solve...
w^4 - 20w^2 - 2 = 0.
It is not qudratic but is to be reduced to a quadratic equation in order for us to solve it. It is said to be reducible to quadratic.
I know we have to substitute u for w^2. So then the equation would be
u^2 - 20u - 2 = 0
Solving for u is...
u = 10 - radical sign 102 and
u = 10 + radical sign 102
I know the solutions are:
10 - radical sign 102 all under the same radical sign ,
10 + radical sign under radical sign 102 all under the same radical sign ,
10 - radical sign under radical sign 102 all under the same negative radical sign ,
10 + radical sign under radical sign 102 all under the same negative radical sign
My question is: Where did they get 10 and 102? I guess I do not know how to solve for u.
Can You please show the steps for this problem?
This does not come from a book.
Thank you!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use the quadratic formula:

which is the general solution to the quadratic equation: .

For your equation:

, so

But , so , and we have:

or

But remember, , so or

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