Algebra question!!!!?

The equation becomes 182 = n^2 - n, which is a quadratic equation. There are many ways to solve this, such as using the quadratic formula, etc. Here, a solution is done using the method of completing the squares:

The equation becomes

n^2 - n = 182. We need to find a number to be added to the left hand side so that it becomes a perfect square. To do that, get the coefficient of n, which is 1. Then divide it by the coefficient of n^2 (which is also 1), then divide it by the constant 2, so that is becomes 1/2. Finally, take its square, which is 1/4. That is the number that you add for each side. The equation then becomes

n^2 - n + 1/4 = 182 + 1/4 = 728/4 + 1/4

=> (n - 1/2)^2 = 729/4

=> n - 1/2 = sqrt(729/4) = +/- 27/2

=> n = 27/2 + 1/2 or n = -27/2 + 1/2

=> n = 14 or -13

Looking back at the problem, we notice that -13 is not a solution. Therefore, the answer is n = 14.

N = 182 =>

182 = n^2 - n =>

n^2 - n -182 = 0

D = 1 + 4*1*182 = 729

n1,2 = (1 +/- 27) /2 =>

n1= 14

n2=-13

=> n=14 (number of teams)

N = n^2 - n

182 = n^2 - n

Algebra

n^2 - n - 182 = 0

(n - 14)(n + 13) = 0

n = 14 or n = -13

Since we are working with teams > 0

n = 14

14 Teams it is!!!

n^2 - n = 182

n^2 - n - 182 = 0

(n - 14)(n + 13) = 0

n = 14 or n = -13

Number of teams can't be negative, so n = 14.

i.e. N = 182,

Therefore....

182 = n^2 - n

182 = 14^2 - 14

n = 14

45.5