Question 682947
Given:
(1) x^2 -2x = 2
Completing the square on the left side of (1) allows us to rewrite (1) as
(2) (x-1)^2 -1 = 2 or
(3) (x-1)^2 = 3
Taking the square root of each side of (3) yields
(4) x-1 = +/- {{{sqrt(3)}}} or the roots of (1) are
(5) x = (1 + {{{sqrt(3)}}}, 1 - {{{sqrt(3)}}}) which gives the factors of (1) as
(6) x^2 -2x -2 = (x-1+{{{sqrt(3)}}})(x-1-{{{sqrt(3)}}})