Question 465939
Given the fact that the number is an integer, we can guess and check by inputting small integer values. Here we will get 2 as our answer. To show that it is the only answer, we can write a quadratic:


*[tex \LARGE 5x + 3x^2 = 22, x \in \mathbb{Z}]


*[tex \LARGE 3x^2 + 5x - 22 = 0]


*[tex \LARGE 3(x-2)(x-C) = 0] where C is the other root.


Here, we expect the constant term, 3(-2)(-C) to equal -22 --> 6C = -22. This implies C = -11/3, not an integer, so 2 is the only integer root.