4x^2+ 5x +2 factor out the 4
4 ( x^2 + (5/4)x + 2/4)
Take (1/2) of (5/4) = 5/8......square it = 25/64...add it and subtract it
4 ( x^2 + (5/4)x + 25/64 + 2/4 - 25/64 )
Factor the first three terms in the parentheses and simplify
4 [ ( x + 5/8)^2 + 32/64 - 25/64 ]
4 [ ( x + 5/8)^3 + 7 / 64]
4 ( x + 5/8)^2 + 7/16