Solicit
wiktionary
From Middle English soliciten, solliciten, from Old French soliciter, solliciter, from Latin sollicitāre, present active participle of sollicitō(“stir, disturb; look after”), from sollicitus(“agitated, anxious, punctilious”, literally “thoroughly moved”), from sollus(“whole, entire”) + perfect passive participle of cieō(“shake, excite, cite, to put in motion”).
etymonline
solicit (v.)
early 15c., soliciten, "to disturb, trouble," from Old French soliciter, solliciter (14c.), from Latin sollicitare "to disturb, rouse, trouble, harass; stimulate, provoke," from sollicitus "agitated," from sollus "whole, entire" (from PIE root *sol- "whole, well-kept") + citus "aroused," past participle of ciere "shake, excite, set in motion" (from PIE root *keie- "to set in motion"). Related: Solicited; soliciting.
The meaning "entreat, petition" is from 1520s. Meaning "to further (business affairs)" evolved mid-15c. from a French sense of "manage affairs." The sexual sense (often in reference to prostitutes) is attested from 1710, probably from a merger of the business sense and an earlier sense of "to court or beg the favor of" (a woman), attested from 1590s.