ANSWER:

You should have completed the second salam and then offered sujood assahu and then offered another salam. 

Due to your ignorance, your prayer is valid.

QUESTION: I forgot the first tashahhud so I had to do sujood as-sahw. However, I forgot to do so right up until I made the first taslim to the right. Upon remembering I Immediately said takbir, did sujood as-sahw and made taslim again. Is my prayer valid

Prayer |