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Related to determinably: determinedly

determine the root of the problem

To find or ascertain the cause of a particular problem or issue. The plumber has determined the root of the problem, and it doesn’t sound too costly to fix, thank goodness.
See also: determine, of, problem, root
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

*root of the problem

an understanding of the causes or basis of a problem. (*Typically: determine ~; figure out ~; find ~; get to ~; get at ~.) It will take a little more study to get to the root of the problem. Let's stop avoiding the issue and get at the root of the problem.
See also: of, problem, root
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.

bound and determined to

Firmly resolved to, as in He was bound and determined to finish the assignment before taking on another. This phrase is a redundancy used for emphasis, as bound and determined here both mean "resolved to." Also see bound to.
See also: and, bound, determined, to
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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References in periodicals archive ?
Nobody knows the latent volcano of the soul of woman nor indeed of man which can erupt suddenly and determinably. Feminism is a reaction of women with guts and steam and nobody tells the other to remove her head from the yoke.
His assistant Mark Venus also had to be restrained at the full-time whistle by that same fourth official, as he made his way determinably onto the pitch to try and remonstrate with the referee.
With all three the first film seems more personal, more serious, more disturbing, more challenging, the second more obviously a crowdpleaser, lighter in tone, with plenty of humour, more ingratiating, as well as more polished (bigger budget), determinably 'clever'.
The point here is that we can have a "nature" and still not be able to determinably establish what that is; nor can we use it as the theoretical ground for defining what is true, beautiful, and good, except for speculative purposes.
According to leaks Sir John's report was especially damning, suggesting that the raid was "authorised on intelligence that was not merely exaggerated but determinably false .
It is a world of tension, conflict, and competition which cannot, finally, be overcome except at a price none but the most determinably utopian and willful--and, finally, anti-democratic--will be prepared to pay.