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!!