succeed vs work out

succeed

verb
  • To prosper or attain success and beneficial results in general. 

  • To ascend the throne after the removal or death of the occupant. 

  • To prevail in obtaining an intended objective or accomplishment; to prosper as a result or conclusion of a particular effort. 

  • To follow something in sequence or time. 

  • To support; to prosper; to promote or give success to. 

  • To descend, as an estate or an heirloom, in the same family; to devolve; (often with to). 

  • To come in the place of another person, thing, or event; to come next in the usual, natural, or prescribed course of things; to follow; hence, to come next in the possession of anything; (often with to). 

  • To come after or follow; to be subsequent or consequent; (often with to). 

  • To replace or supplant someone in order vis-à-vis an office, position, or title. 

work out

verb
  • To succeed; to result in a satisfactory situation. 

  • To make sense of. 

  • To strengthen a part one’s body by exercise. 

  • To earn a wage working away from one's farm. 

  • To bring about or cause to happen by work or effort. 

  • To conclude with the correct solution. 

  • To remove all the mineral that can be profitably exploited. 

  • To smooth or perfect. 

  • To exercise, especially by lifting weights. 

  • Used other than figuratively or idiomatically: see work, out. 

  • To calculate. 

How often have the words succeed and work out occurred in a corpus of books? (source: Google Ngram Viewer )