TeX source:

\begin{aligned} \mathrm{KE}_{\text {int }}^{\prime} &=\frac{1}{2} m_{1} v_{1}^{\prime 2}+\frac{1}{2} m_{2} v_{2}^{\prime 2} \\ &=\frac{1}{2}(0.350 \mathrm{~kg})(-4.00 \mathrm{~m} / \mathrm{s})^{2}+\frac{1}{2}(0.500 \mathrm{~kg})(3.70 \mathrm{~m} / \mathrm{s})^{2} \\ &=6.22 \mathrm{~J} \end{aligned}