rahul, alternate method by differentitaion could be, p= 5x^2+11(8-x)^2
further dp/dx = 32x-176 =>dp/dx=0gives x=11/2
d2p/dx2 =32 which is positive, means minima exists at dp/dx,
put x=11/2 and get the value as 220.
you can also follow method od quadratic equations as mentioned by Ramesh, cheers ramesh!!