SOLUTION: Im not quite understanding this question. x^−2+15x^-1+56=0

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Question 1119850: Im not quite understanding this question. x^−2+15x^-1+56=0
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2Fx%29%5E2%2B15%281%2Fx%29%2B56=0

letv=1%2Fx;

v%5E2%2B15v%2B56=0

v=%28-15%2B-+sqrt%2815%5E2-4%2A56%29%29%2F2

v=%28-15%2B-+sqrt%281%29%29%2F2

v=%28-15%2B-+1%29%2F2

system%28v=-7%2Cor%2Cv=-8%29
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Now backsubstitute v for each of these and solve for x.
system%281%2Fx=-7%2C+or%2C+1%2Fx=-8%29;

system%28highlight%28x=-1%2F7%29%2Cor%2Chighlight%28x=-1%2F8%29%29
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You could also check for possible factorization at the beginning:
%281%2Fx%29%5E2%2B15%281%2Fx%29%2B56=0
%28%281%2Fx%29%2B7%29%28%281%2Fx%29%2B8%29=0------and solve for 1%2Fx from here.