To solve the equation x² – x – 2 = 0, we can factor it. We are looking for two numbers that multiply to -2 (the constant term) and add up to -1 (the coefficient of x).
These two numbers are -2 and +1. Thus, we can factor the equation as follows:
x² - x - 2 = (x - 2)(x + 1) = 0
Now, we can set each factor to zero to find the solutions:
x - 2 = 0 => x = 2
x + 1 = 0 => x = -1
Therefore, the solutions to the equation are x = 2 and x = -1. In terms of the set notation, we can express the solution set as:
{-1, 2}
So, the set of all real numbers x that satisfy the equation x² – x – 2 = 0 is {-1, 2}.