Show that x^2 - x +2 is positive for all values of x

(x-1/2)² = (x-1/2)(x-1/2)=x²-x+1/4, add 7/4 to get x²-x+2 therefore x²-x+2 = (x-1/2)² + 7/4

squared numbers always positive so (x-1/2)² >= 0 therefore (x-1/2)² + 7/4 is always positive