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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
u%5E2+-+20u+-+2+=+0

Use the quadratic formula:

u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ which is the general solution to the quadratic equation: au%5E2%2Bbu%2Bc=0.


For your equation:
a=red%281%29
b=green%28-20%29
c=blue%28-2%29, so


u+=+%2820+%2B-+sqrt%28400%2B8%29%29%2F%282%29
u+=+%2820+%2B-+sqrt%28408%29%29%2F%282%29

But 408=4%2A102, so sqrt%28408%29=sqrt%284%29%2Asqrt%28102%29=2%2Asqrt%28102%29, and we have:

u+=+10+%2B+sqrt%28102%29 or u+=+10+-+sqrt%28102%29

But remember, u=w%5E2, so w=+%2B+sqrt%28u%29 or w+=+-sqrt%28u%29

w=%2Bsqrt%2810+%2B+sqrt%28102%29%29
w=%2Bsqrt%2810+-+sqrt%28102%29%29
w=-sqrt%2810+%2B+sqrt%28102%29%29
w=-sqrt%2810+-+sqrt%28102%29%29