Solve for x?
2x2+4x+1=0, divide through by 2:
x2+2x+½=0, complete the square:
x2+2x+1-½=0,
(x+1)2-½=0, (difference of two squares),
(x+1-√½)(x+1+√½)=0⇒x=-1+√½ or x=-1-√½. The quadratic formula gives the same result.
x=-1+√2/2 or -1-√2/2 is the rationalised solution.