SOLUTION: How do I algebraically find x when x^4=16?

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Question 74699: How do I algebraically find x when x^4=16?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4=16 subtract 16 from both sides
x%5E4-16=0 Note that this can be factored. (We'll break the quartic equation into two quadratic equations and we know how to solve those).
%28x%5E2-4%29%28x%5E2%2B4%29=0 so we have
%28x%5E2-4%29=0 note that this can be factored
%28x%2B2%29%28x-2%29=0
x=%2B2 --------------------------------------Ans#1
and
x=-2------------------------------------------Ans#2
%28x%5E2%2B4%29=0 Actually this can be factored also
%28x%2B2i%29%28x-2i%29=0
x=%2B2i-----------------------------------------Ans#3
and
x=-2i----------------------------------------Ans#4
Lets look at solving the two quadratics in another way:
x%5E2-4=0 add 4 to both sides
x%5E2=4 take sqrt of both sides
sqrt%28x%5E2%29=sqrt%284%29 or
x=%2B2
x=-2
and
x%5E2%2B4=0 subtract 4 from both sides
x%5E2=-4 take the sqrt of both sides
sqrt%28x%5E2%29=sqrt%28-4%29 or
x=%2B2i
x=-2i

Hope this helps---ptaylor