If you have to solve it by completing the square, first move the known term to the right of equal with changed sign.
x² - x = 2
We have to divide the term "b" (-x) by 2 and sqaure it and then add it to the left of equal and to the right of equal.
x² - x + (1/2)² = 2 + (1/2)²
Now, if we look carefully, x² - x + (1/2)² is a square of a binomial, x² is the square of x and (1/2)² is the square of 1/2 so...
(x - 1/2)² = 2 + (1/2)²
(x - 1/2)² = 2 + 1/4
(x - 1/2)² = 9/4
Final answer: (x - 1/2)² = 9/4