Completion of a local noetherian $\Gamma$-algbera

Question

I am in trouble with a result . Let $\Gamma$ is a complete local noetherian $k$-algbera with residue field $k$ and $(R,m)$ is a local noetherian $\Gamma$-algebra with residue field $k$. Also let $\hat{R}$ is the completion of $R$ then we know that $$\hat{R} \cong \Gamma[[ X_1,...,X_d]] / J$$ where $\Gamma[[ X_1,...,X_d]]$ is the formal power series on $d$ variables for some $d$ and $J$ is some ideal .

Question:

1. Why $J$ is supposed to be in the ideal $(X_1,...,X_d)^2$ ?

2 . What is a presentation of the $m$-adic completion $\hat{R}$ ?

Edit: This is actually Proposition $2.1.1 (ii)$ page $38$ - Book : Deformation of algebraic schemes - Sernesi.

Thank you in advance.