The sum of half a number and that number's reciprocal is the same as 51 divided by the number. The number is negative. Find the number.

Question

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Answer 1

if x = the number then 1/x equals the reciprocal

 

x/2 + 1/x = 51/x    multiply by 2x

 

x² + 2 = 102

 

x² = 100

 

because the number must be negative, x = -10

 

to check:

-10/2 + -1/10 = -51/10

-5 + -.1 = -5.1 checks