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Suppose the decimal 0.28 is equal to {1}{n}+{2}{n^2}, where n is negative. Find  n.

 May 5, 2019
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1(n) + 2(n^2)   =  0.28

 

2n^2  + n  - 0.28  = 0      [ multiply through by 100 ]

 

200n^2 + 100n - 28  = 0

 

50n^2 + 25n - 7   = 0

 

(5n - 1)(10n + 7)  = 0

 

Only the second factor will produce a negative n

 

10n + 7  = 0

 

10n  = -7

 

n  = -7/10

 

 

 

cool cool cool

 May 5, 2019

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