How many teams are in a league if each team plays each other team once, and their are 28 games?

Question

How would you solve that question using the formula G(n)=(n^2-n/2)/2? (Solving by completing the square)

Answer 1

Using Yefim's equation from above, we can complete the square as follows:

x² - x - 56 = 0

x² - x = 56

(x² - x + 1/4) = 56 + 1/4

(x - 1/2)² = 225/4

x - 1/2 = √(225/4)

x - 1/2 = 15/2

x = 15/2 + 1/2

x = 16/2

x = 8

Hope this helps!

Answer 2

x(x - 1)/2 = 28, x² - x - 56 = 0, (x - 8)(x + 7) = 0 So x = 8 teams