SOLUTION: I need help with this problem. solve x^4+10x^2+9=0 Thank you!

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Question 481460: I need help with this problem.
solve x^4+10x^2+9=0
Thank you!
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
You can use a temporary substitution in which z+=+x%5E2, so...
x%5E4%2B10x%5E2%2B9+=+0 Substitute z+=+x%5E2
z%5E2%2B10z%2B9+=+0 Factor.
%28z%2B1%29%28z%2B9%29+=+0 Apply the "zero product" rule.
z%2B1+=+0 or z%2B9+=+0 so that...
z+=+-1 or z+=+-9 Now replace the temporary variable z with z+=+x%5E2 to get:
x%5E2+=+-1 or x%5E2+=+-9 and so...
x+=+sqrt%28-1%29, x+=+-sqrt%28-1%29, or x+=+sqrt%28-9%29, x+=+-sqrt%28-9%29 But these can be simplified to...
x+=+i, x+=+-i or x+=+3i, x+=+-3i where i+=+sqrt%28-1%29