Question

2x² +4x+1=0

Answer 1

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.