Question

There are two factors of -36 such that one factor is 11 less than half of the other factor. Choose all the pairs of these factors.

Answer 1

x*y=-36 and x=(1/2)y-11

substitute the second eqn into the first eqn
[(1/2)y-11]y=-36

distribute, bring everything to one side and simplify
(1/2)y^2-11y+36=0

I'm going to multiply both sides by two to make my factoring easier.
y^2-22y+72=0

(y-4)(y-18)=0
y=4, y=18

using one of the original equations above
x=(1/2)(4)-11=-9 when y is 4
x=(1/2)(18)-11= -2 when y is 18

so... two pairs of factors satisy the given condition
4 with -9 and 18 with -2