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
PM
(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
