SOLUTION: A scientist wants to research the potential spread of germs by contact. She knows that the number of possible handshakes within a group of "X" people is given by the equation:

Question 385423: A scientist wants to research the potential spread of germs by contact. She knows that the number of possible handshakes within a group of "X" people is given by the equation:
N= 1/2(X^2(two meaning squared)-X) or N=1/2(X^2-X) looks better.
N= 1/2 (x squared minus x)
N= 78 (Number of possible handshakes)
I know the answer is 13, but I can't figure out the steps to come to that. I under stand that the X squared is the number of people shaking hands with everyone else minus one person because they don't shake hands with themselves. I also understand that multiplying it times .5 or 1/2 is because they only shake one hand of each person, but other than starting to guess numbers that make X, I can't figure out the steps to get 13.
Thanks!
Janet
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
N= 1/2 (x squared minus x)
N= 78
------
Solve for "x":
(1/2)(x^2-x) = 78
x^2-x = 156
---
x^2-x-156 = 0
Factor:
(x+12)(x-13) = 0
Positive solution:
x = 13
=======
Cheers,
Stan H.
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