SOLUTION: the sum of a number and 24 times its reciprocal is -11. find the number.

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Question 958656: the sum of a number and 24 times its reciprocal is -11. find the number.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x=the number
x%2B24%2Fx=-11 Multiply each side by x.
x%5E2%2B24=-11x Add 11x to each side.
x%5E2%2B11x%2B24=0
%28x%2B3%29%28x%2B8%29=0
x%2B3=0 or x%2B8=0
x=-3 or x=-8 ANSWER The number is -8 or -3.
CHECK:
For (-3):
x%2B24%2Fx=-11
-3%2B%2824%2F-3%29=-11
-3%2B%28-8%29=-11
-11=-11
For (-8):
x%2B24%2Fx=-11
-8%2B%2824%2F-8%29=-11
-8%2B%28-3%29=-11
-11=-11