Quadratic equation

Question

Out of a group of goats, 2 times the square root of the number of goats were kept in shade, (1/4) of them were taken for grazing and 15 were sold, find the initial number of goats.

 

 

 

 

Answer is supposed to be: 36 goats.

Answer 1

2*sqrt(N) + N/4 + 15 = N

 

2*sqrt(N) = N - N/4 - 15

 

2*sqrt(N) = (3/4)N - 15

 

 

sqrt(N) = (3/8)N - (15/2)

 

N = (9/64)N^2 - 2(3/8)(15/2)N + (225/4)

 

0 = (9/64)N^2 - (45/8)N + (225/4)

 

0 = 9N^2 - 360N + 900

 

N = [  -(-360) +or-  sqrt ( (-360)(-360) - 4(9)(900))]/(2*9)

 

   = [  360 +or- sqrt ( 97200)]/18

 

  = [ 360 +or- 311.76914536239.......]/18

 

 

The positive branch of this solution when rounded leads to 37 goats

while the negative branch makes no sense at all.

 

2*sqrt(37) = 12

1/4 of 35 = 9

    That leaves 15 , which were sold.