SOLUTION: solve, x^4-12x^2-45=0

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Question 120029: solve, x^4-12x^2-45=0
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=x%5E2 to get




w%5E2-12w-45=0

%28w-15%29%28w%2B3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
w-15=0 or w%2B3=0

w=15 or w=-3 Now solve for w in each case


Remember, we let w=x%5E2, so this means



x%5E2=15 or x%5E2=-3



Now take the square root of both sides in each case



x=0%2B-sqrt%2815%29 or x=0%2B-sqrt%28-3%29


Simplify

x=0%2B-sqrt%2815%29 or x=0%2B-sqrt%283%29%2Ai


Now break up the plus/minus


x=sqrt%2815%29, x=-sqrt%2815%29, x=sqrt%283%29%2Ai or x=-sqrt%283%29%2Ai



So our answers are


x=sqrt%2815%29, x=-sqrt%2815%29, x=sqrt%283%29%2Ai or x=-sqrt%283%29%2Ai