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to bring to a successful end; carry through; accomplish:
The police crackdown on speeders achieved its purpose.
to get or attain by effort; gain; obtain:
to achieve victory.
to bring about an intended result; accomplish some purpose or effect.
Contemporary Examples

Those who wish to begin a Tsa Lung practice, which is an advanced but achievable discipline, are encouraged to seek a teacher.
Can Meditation Cure Disease? Maureen Seaberg December 24, 2010

In Yes You Can: The achievable Diet, Diana Le Dean searches for the silent killers and suggests alternatives.
How to Watch Out for Hidden Sugar and Replace With Leaner Substitutes Diana Le Dean February 22, 2013

I find myself mostly in the realist camp, looking hard at achievable goals and usable power.
We Need Liberals Now! Leslie H. Gelb October 27, 2011

How to solve it or what the administration believes is achievable in Afghanistan remains, like so much else, to be determined.
Joe Biden’s Empty Words Mark Salter February 9, 2009

This article has been adapted from Yes You Can: The achievable Diet by Diana Le Dean.
How to Watch Out for Hidden Sugar and Replace With Leaner Substitutes Diana Le Dean February 22, 2013

Historical Examples

But with such stability the expansion and balanced growth of international trade is not achievable.
After the Rain Sam Vaknin

Everything is possible; but without labour and failure nothing is achievable.
David Elginbrod George MacDonald

Only by the possession of treasures these things are achievable, therefore it is laudable in man to strive after wealth.
Fairy Tales From all Nations Anthony R. Montalba

There was not much of the night left in which to sleep, even had a semblance of sleep been achievable.
The Glimpses of the Moon Edith Wharton

It was inconceivable that it could be the practical and achievable cunning of military bullies and strategists.
Out To Win Coningsby Dawson

verb (transitive)
to bring to a successful conclusion; accomplish; attain
to gain as by hard work or effort: to achieve success
v.

early 14c., from Old French achever (12c.) “to finish, accomplish, complete,” from phrase à chef (venir) “at an end, finished,” or Vulgar Latin *accapare, from Late Latin ad caput (venire); both the French and Late Latin phrases meaning literally “to come to a head,” from stem of Latin caput “head” (see capitulum).

The Lat. caput, towards the end of the Empire, and in Merov[ingian] times, took the sense of an end, whence the phrase ad caput venire, in the sense of to come to an end …. Venire ad caput naturally produced the Fr. phrase venir à chef = venir à bout. … From this chief, O.Fr. form of chef (q.v.) in sense of term, end, comes the Fr. compd. achever = venir à chef, to end, finish. [Auguste Brachet, “An Etymological Dictionary of the French Language,” transl. G.W. Kitchin, Oxford, 1878]

Related: Achieved; achieving.