carry through

English

(transitive, idiomatic) To manage to execute; to perform successfully, all the way to the end.
- 2006, Michael Bodin, Primer of Relativity: A Student's Introduction, page 66:
  He was clearly dealing with extremely small quantities, and considering the clumsy structure of telescopes then in use, it is surprising he managed to carry through the procedure at all. Nevertheless, he obtained a remarkably good value […]

perform successfully to the end