Consider the digital control system

\[
\mathbf{x}[(k+1) T]=\mathbf{A} \mathbf{x}(k T)+\mathbf{B} u(k T)
\]

where

\[
\mathbf{A}=\left[\begin{array}{cc}
0 & -1 \\
-1 & -1
\end{array}ight], \quad \mathbf{B}=\left[\begin{array}{l}
0 \\
1
\end{array}ight]
\]

The state feedback control is described by \(u(k T)=-\mathbf{K x}(k T)\), where

\[
\mathbf{K}=\left[\begin{array}{lll}
k_{1} & k_{2}
\end{array}ight] .
\]

Find the values of \(k_{1}\) and \(k_{2}\) so that the roots of the characteristic equation of the closed-loop system are at 0.5 and 0.7 .