Can I take my ex girlfriend back?

We were together and living in relationship for two years. I found out that she was cheating behind me. Initially she denied and later apologized. Few months after, I caught her red-handed with her colleague. She requested me to give her another chance but I broke up with her.
In last six months, I dated couple of girls but didn't click. I still have strong feelings for my ex. She is continuously chasing me and trying to get get back to me. Some days she sends about twenty odd texts though I don't reply. Shall I take her back? I am utterly confused..
Can I take my ex girlfriend back?
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