con- (expressing completion) + quaerere ‘seek’

source: [世界征服 謀略のズヴィズダーのヴィニエイラのGIF画像｜無料GIF画像検索 GIFMAGAZINE 40440]

overcome and take control of (a place or people) by use of military force:

〈人･国などが〉〈敵･国〉を征服する; (征服して)〈領土〉を獲得する; (試合で)〈相手〉を打ち負かす

e.g. the Magyars conquered Hungary in the Middle Ages.

successfully overcome (a problem or weakness):

〈人が〉〈病気･困難･障害など〉を克服する; 〈感情〉を抑える

e.g. a fear she never managed to conquer.

climb (a mountain) successfully:

〈(未登頂の)山〉を征服する

e.g. the second American to conquer Everest.

gain the love, admiration, or respect of (a person or group of people):

｟主に文｠ 〈名声･称賛･愛など〉を得る, 獲得する; 〈異性〉を口説き落とす

e.g. the Beatles were to leave Liverpool and conquer the world.

conquerable | ˈkäNGk(ə)rəb(ə)l | adjective

Middle English (also in the general sense ‘acquire, attain’): from Old French conquerre, based on Latin conquirere ‘gain, win’, from con- (expressing completion) + quaerere ‘seek’.