SOLUTION: Solve a) x^4 - 29x^2 + 100 = 0 Thank you so much in advance:)

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Question 828144: Solve
a) x^4 - 29x^2 + 100 = 0
Thank you so much in advance:)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-+29x%5E2+%2B+100+=+0 may look difficult,
but I bet you could solve y%5E2+-+29y+%2B+100+=+0 somehow.
If you look closely, you will notice that making y=x%5E2 you get y%5E2=x%5E4,
and substituting those expressions one equation turns into the other equation.

I would solve y%5E2+-+29y+%2B+100+=+0 by factoring:
y%5E2+-+29y+%2B+100+=+0
%28y-4%29%28y-25%29=0 --> system%28highlight%28y=4%29%2C%22or%22%2Chighlight%28y=25%29%29
Maybe you would solve it by applying the quadratic formula:
y=%28-%28-29%29+%2B-+sqrt%28%28-29%29%5E2-4%2A1%2A100+%29%29%2F%282%2A1%29+
y=%2829+%2B-+sqrt%28841-400%29%29%2F2
y=%2829+%2B-+sqrt%28441%29%29%2F2
y=%2829+%2B-+21%29%2F2 -->

Either way you end up with
x%5E2=4 --> system%28highlight%28x=-2%29%2C%22or%22%2Chighlight%28x=2%29%29
or
x%5E2=25 --> system%28highlight%28x=-5%29%2C%22or%22%2Chighlight%28x=5%29%29

The short way to write the solution to the equation is:
x%5E4+-+29x%5E2+%2B+100+=+0
%28x%5E2-4%29%28x%5E2-25%29=0
%28x-2%29%28x%2B2%29%28x-5%29%28x%2B5%29=0 -->