Complete the square:
2x^2+8x+1
Maybe it would help if it was written like this
$\displaystyle \displaystyle \begin{align*} 2(x^2 + 4x) + 1 &= 2(x^2 + 4x + 2^2 - 2^2) + 1 \\ &= 2(x^2 + 4x + 4 - 4) + 1 \\ &= 2(x^2 + 4x + 4) + 2(-4) + 1 \\ &= 2(x^2 + 4x + 4) - 8 + 1 \end{align*}$