\(0 = \frac{{{m_1}\left( { - {x_1}} \right) + {m_2}{x_2}}}{{{m_1} + {m_2}}} \Rightarrow {m_1}{x_1} = {m_2}{x_2}\,\,\,\,\,...\left( 1 \right)\)

Finally, 

The centre of mass is at the origin

\(\therefore 0 = \frac{{{m_1}\left( {d - {x_1}} \right) + {m_2}\left( {{x_2} - d'} \right)}}{{{m_1} + {m_2}}}\)

\(\begin{array}{l}
 \Rightarrow 0 = {m_1}d - {m_1}{x_1} + {m_2}{x_2} - {m_2}d'\\
 \Rightarrow d' = \frac{{{m_1}}}{{{m_2}}}d\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[Form\,\left( 1 \right).]
\end{array}\)