SOLUTION: How do I answer this? Solve the inequality. x^4 - 32x^2 - 144 > 0

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Question 362439: How do I answer this?
Solve the inequality.
x^4 - 32x^2 - 144 > 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-+32x%5E2+-+144+%3E+0
%28x%5E2-36%29%28x%5E2%2B4%29%3E0
%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0
Break up the number line into 4 regions using the critical points of the function.
Region 1:(-infinity,-6)
Region 2:(-6,0)
Region 3:(0,6)
Region 4:(6,infinity)
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For each region, choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
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Region 1:x=-7
%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0
%28-7-6%29%28-7%2B6%29%28%28-7%29%5E2%2B4%29%3E0
%28-13%29%28-1%29%2853%29%3E0+
689%3E0+
True, Region 1 is part of the solution region.
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Region 2:x=-1
%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0
%28-1-6%29%28-1%2B6%29%28%28-1%29%5E2%2B4%29%3E0
%28-7%29%285%29%285%29%3E0+
-175%3E0+
False, Region 2 is part of the solution region.
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Region 3:x=1
%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0
%281-6%29%281%2B6%29%28%281%29%5E2%2B4%29%3E0
%28-5%29%287%29%285%29%3E0+
-175%3E0+
False, Region 3 is not part of the solution region.
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Region 4:x=7
%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0
%287-6%29%287%2B6%29%28%287%29%5E2%2B4%29%3E0
%281%29%2813%29%2853%29%3E0+
689%3E0+
True, Region 4 is part of the solution region.
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Solution Region: (-infinity,-6) U (6,infinity)
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Graphical verification: Look for regions where the function is above the x-axis (y%3E0)
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