Perhaps this would be easiest by completing the square...
Move the constant to the other side by adding 1 to both sides
x^2-x=1 halve the linear coefficient, square it, and add it to both sides, (-1/2)^2=1/4
x^2-x+1/4=5/4 now the left side is a perfect square
(x-1/2)^2=5/4 take the square root of both sides
x-1/2=±√(5/4) now add 1/2 to both sides
x=1/2±√(5/4)
x=(1±√5)/2
so the factors are:
(x+1/2+√(5/4))(x+1/2-√(5/4))
