\documentclass[12pt]{article}
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\begin{document}
\begin{equation*}
  \aligned 
    P[k+1] &= E\{(x[k+1] - \hat x[k+1]) (x[k+1] - \hat x[k+1])^T\} \\
    &= (A - LC) P[k] (A - LC)^T + F R_v F^T + L R_w L^T \\
    &= A P[k] A^T + F R_v F^T - A P[k] C^T L^T - L C P[k] A^T \\
    & \qquad + L (R_w + C P[k] C^T) L^T.
  \endaligned
\end{equation*}
\end{document}