Exegesis:

eipen de pros tēn gunaika ‘but he said to the woman,’ without indication of the change of subject. de suggests that Jesus did not reply to what the other guests thought or said.

hē pistis sou sesōken se ‘your faith has saved you.’ This phrase usually occurs at the conclusion of some healing story (cf. 8.48; 18.42; Mt. 9.22; Mk. 5.34). The present context requires a different meaning for sesōken, i.e. has saved you from the power of sin.

poreuou eis eirēnēn ‘go in peace,’ a quotation from 1 Sam. 1.17, occurring, with a different verb also in Mk. 5.34.

Translation:

Your faith has saved you, or, ‘you are saved (or, God has saved you) because you have believed (in me).’ In this context Tboli renders “your faith” by ‘that you did not doubt (lit. not being-two your breath)’; cf. also on 8.48.

Go in peace is to be rendered by an idiomatic expression of farewell, implying well-wishing, e.g. ‘with one heart go,’ also used commonly as reassurance (Tzeltal), ‘go well’ (Zarma), ‘there now, return now’ (Tboli), salaam (Kele). The translator should not try to bring in the term for ‘peace’ as used e.g. in 1.79 (which see), unless it fits the idiom.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.