Diagonalization & Matrix Powers · Hard problem

Two proportions $x_1(t)$ and $x_2(t)$ satisfy $\mathbf{x}' = Q\mathbf{x}$ with $Q = \begin{pmatrix}-2 & 1\\2 & -1\end{pmatrix}$ and $\mathbf{x}(0) = \begin{pmatrix}1\\0\end{pmatrix}$. At what time $t$ does $x_1(t)$ equal $\tfrac12$?