SOLUTION: 3x^-2-27x^-1+42=0 I need help solving for u and back substituting for x. I would appreciate your help. Thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 3x^-2-27x^-1+42=0 I need help solving for u and back substituting for x. I would appreciate your help. Thanks      Log On


   

Question 61072: 3x^-2-27x^-1+42=0
I need help solving for u and back substituting for x. I would appreciate your help. Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can temporarily substitute u for x%5E%28-1%29, so rewriting the equation:
3u%5E2+-+27u+%2B+42+=+0 Start by factoring a 3.
3%28u%5E2+-+9u+%2B+14%29+=+0 Aplying the zero product principle:
u%5E2+-+9u+%2B+14+=+0 Factor the the left side:
%28u+-+2%29%28u+-+7%29+=+0 Apply the zero product principle:
u+-+2+=+0 and/or u+-+7+=+0
u = 2 and/or u = 7 Now replace the x%5E%28-1%29 for u.
x%5E%28-1%29+=+2
1%2Fx+=+2
1+=+2x
x+=+1%2F2
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x%5E%28-1%29+=+7
1%2Fx+=+7
1+=+7x
x+=+1%2F7