Placate, soothe (7)
I believe the answer is:
mollify
I believe this is a double definition.
'placate' is the first definition.
(synonyms)
'soothe' is the second definition.
(thesaurus)
(Other definitions for mollify that I've seen before include "Appease the anger of (someone)" , "Placate, appease" , "Soothe feelings of" .)