To solve this cubic equation, we can try factoring or using the rational root theorem.

Factoring:

The equation can be rewritten as:
x^3 - x^2 - 25x + 2 = 0

We can group the terms as:
x^2(x - 1) - 25(x - 1) = 0

This simplifies to:
(x^2 - 25)(x - 1) = 0

Now we can factor further:
(x + 5)(x - 5)(x - 1) = 0

So the roots of the equation are x = -5, x = 5, and x = 1.

Therefore, the solutions to the cubic equation x^3 - x^2 - 25x + 2 = 0 are x = -5, x = 5, and x = 1.