SOLUTION: A number is ten less than twice another number and the sum of their reciprocals is -1/4 what pairs of numbers satisfy this condition

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Question 1128947: A number is ten less than twice another number and the sum of their reciprocals is -1/4 what pairs of numbers satisfy this condition
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The numbers:
x
and
2x-10


1%2Fx%2B1%2F%282x-10%29=-1%2F4
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4%282x-10%29%2B4x=-x%282x-10%29
8x-40%2B4x=-2x%5E2%2B10x
12x-40=-2x%5E2%2B10x
-2x%5E2-2x%2B40=0
x%5E2%2Bx-20=0---------this is factorable.
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