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Show $($step by step$)$ that the clustering assignment problem

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$\backslash$pi$($i$)=\backslash$arg$\backslash$min$\_\{$j$=1,\backslash$ldots$,$ k$\}\backslash |$x$^$i$-$ c$^$j$\backslash |^2$

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is equivalent to solving

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$\backslash$pi$($i$)=\backslash$arg $\backslash$min$\_\{$j$=1,\backslash$ldots$,$ k$\}($c$^$j$)^$T$\backslash$left$(\backslash$frac $12$ c$^$j$-$x$^$i$\backslash$right$).$

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