SOLUTION: Find the solutions:x^4-x^2+14=56

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Question 307531: Find the solutions:x^4-x^2+14=56
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
x%5E4-x%5E2%2B14+=+56 Subtract 56 from both sides.
x%5E4-x%5E2-42+=+0 Notice that you now have a quadratic equation in x%5E2
%28x%5E2%29%5E2-%28x%5E2%29-42+=+0 Factor this.
%28%28x%5E2%29%2B6%29%28%28x%5E2%29-7%29+=+0 Apply the zero product rule.
x%5E2%2B6+=+0 or x%5E2-7+=+0 so that...
If x%5E2%2B6+=+0 then...
x%5E2+=+-6 and x+=+sqrt%28-6%29 or x+=+-sqrt%28-6%29
If x%5E2-7+=+0 the...
x%5E2+=+7 and x+=+sqrt%287%29 or x+=+-sqrt%287%29
The roots are:
x+=+sqrt%286%29i where: i+=+sqrt%28-1%29
x+=+-sqrt%286%29i
x+=+sqrt%287%29
x+=+-sqrt%287%29