Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 intransitive verb To find an answer to, explanation for, or way of dealing with (a problem, for example).
 intransitive verb To solve an equation.
from The Century Dictionary.
 noun Solution.
 To loosen; disentangle; unravel; hence, to explain or clear up the difficulties in; resolve; explain; make clear; remove perplexity from: as, to
solve a difficulty, a puzzle, or a problem.  To determine; put an end to; settle.
 To determine or work out by rule; operate on by calculation or mathematical processes, so as to bring out the required result: as, to
solve a problem in mathematics.  To dissolve; melt.
from the GNU version of the Collaborative International Dictionary of English.
 transitive verb To explain; to resolve; to unfold; to clear up (what is obscure or difficult to be understood); to work out to a result or conclusion.
 noun obsolete A solution; an explanation.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 verb To find an
answer orsolution to a problem or question; towork out .  verb mathematics To find the
values ofvariables thatsatisfy a system ofequations and/orinequalities .  verb mathematics To
algebraically manipulate an equation or inequality into a form thatisolates a chosen variable on one side, so that the other side consists of an expression that may be used to generatesolutions .  noun obsolete A
solution ; anexplanation .
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 verb find the solution
 verb settle, as of a debt
 verb find the solution to (a problem or question) or understand the meaning of
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

Too often the result of such instruction is students who can add when told to add, or solve quadratic equations when told to �solve the following quadratic equations,� but cannot decide when to use these techniques in solving problems.
Archive 20080301 Jim Horn 2008

Too often the result of such instruction is students who can add when told to add, or solve quadratic equations when told to �solve the following quadratic equations,� but cannot decide when to use these techniques in solving problems.
Noddings Commentary Jim Horn 2008

I want to travel, see the sites, maybe solve some  "She almost said _solve some murders_, but finished lamely,"  solve some problems in magnesium technology. "

Always, the main problem to solve is to help the user to find "the needle in the haystack".
Archive 20080101 2008

Always, the main problem to solve is to help the user to find "the needle in the haystack".

Israel's foreign minister has suggested that France and Spain solve Europe's problems before lecturing his country on how to deal with the IsraeliArab conflict.
Israeli FM: Europe Should Solve Own Problems Before Ours 2010

Israel's foreign minister has suggested that France and Spain solve Europe's problems before lecturing his country on how to deal with the IsraeliArab conflict.
Israeli FM: Europe Should Solve Own Problems Before Ours 2010

Levy also says that along with scheduling, figuring out the mystery that the grown up Hardy boys need to solve is also a key element to figure out before moving forward.

A brilliant puzzle that no one can solve is called a “failure.”

A brilliant puzzle that no one can solve is called a “failure.”
Archive 20090401 2009
yarb commented on the word solve
In North American sports reporting, to score against for the first time in a game:
"Taylor Pyatt finally solved Detroit netminder Chris Osgood at 2:27 of the second, pouncing on a loose puck after he and Kyle Wellwood forced little Wing Jiri Hudler into a turnover in his own slot area."
 Canucks ride high after fourth straight win, Vancouver Sun, 112508.
Taylor Pyatt, a great hockey name.
November 26, 2008
bilby commented on the word solve
What language is this?
April 19, 2009
gangerh commented on the word solve
One of the simplest copy writing formulas is to state the customer's problem, tell them you can solve it and then tell them precisely how you're going to solve it.
'15 words that will make you money'
July 24, 2009