How to solve this equation with matrices can you please give me some hints to solve the following? I really don't know how to start.
$$X^2= \begin{pmatrix}
6 & 2 \\ 3 & 7
\end{pmatrix}.$$
I tried to express this matrix as $4\cdot I + \begin{pmatrix}
2 & 2 \\ 3 & 3
\end{pmatrix}$ And somehow solve it, but I really have no clue. Please some help.

We have
$$
\begin{pmatrix}
6 & 2 \\ 3 & 7
\end{pmatrix} = QDQ^{-1}$$
where
$$
Q = \begin{pmatrix} -1 & 2 \\ 1 & 3 \end{pmatrix},\  D = \begin{pmatrix} 4& 0 \\ 0 & 9 \end{pmatrix}.
$$
It follows that we may take any of the four matrices
$$
X = Q\begin{pmatrix} \pm 2 & 0 \\ 0 & \pm 3 \end{pmatrix} Q^{-1}.
$$
