  In this paper we establish a formula for computing $d_2(sq^i(x))$ where $x$
is a permanent cycle in the $C_2$-equivariant Adams spectral sequence or the
motivic Adams spectral sequence over $Spec(\mathbb{R})$.
  This requires establishing that the Adams towers have an
$H_{\infty}$-structure as well as determining the attaching maps for
$C_2$-equivariant projective spaces.
  The attaching maps of $C_2$-equivariant projective spaces can then be used to
determine the coefficients of differentials in both the equivariant and motivic
case.
  At the end some sample computations are given.
