To exercise; or to find a solution; or for something to end successfully.
To exercise the body in order to improve fitness; to find a solution to a problem through thinking or effort; or for a situation or plan to end in a successful or satisfactory way.
Type
Separable
Collocations
work out a solution — figure something out
work out at the gym — exercise
work out the details — clarify specifics
⚠️ Watch out
Can mean solve, exercise, or turn out well depending on context — make sure the surrounding sentence makes the intended meaning clear.
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In October 1962, U.S. President John F. Kennedy faced what many historians consider the most {{dangerous|adjective|easy}} thirteen days of the Cold War. Soviet nuclear missiles had been secretly installed in Cuba, just 90 miles from Florida. Kennedy's military advisors {{pushed|verb-various-tenses|easy}} hard for immediate air strikes and a ground invasion. {{Instead|connective|easy}}, Kennedy rejected the fastest solution and demanded his team work through every option. He {{secretly|adjective|medium}} corresponded directly with Soviet Premier Nikita Khrushchev, {{proposing|verb-various-tenses|medium}} a naval blockade rather than an attack, and offering to quietly remove American missiles from Turkey in exchange. On October 28th, Khrushchev agreed to withdraw the Cuban missiles. The invasion never happened. No nuclear weapon was fired. {{What made the difference|connective|hard}} was Kennedy's insistence on slowing down, examining the problem from every angle, and {{negotiating|verb-various-tenses|hard}} rather than striking — a {{high-stakes|adjective|hard}} reminder that when the pressure is greatest, taking the time to properly {{work out|phrasal-verb|medium}} a solution can change everything.
To resolve or figure out a problem means to find a solution or reach a clear answer through thought, discussion, or effort. It implies an active process of working through a difficulty until it is understood or settled.
Type
Verb phrase (transitive)
Collocations
figure out the problem — most common neutral collocation, used when identifying and solving a difficulty
resolve the issue — slightly more formal within neutral range, common in journalism and professional contexts
figure out a solution — emphasises the discovery aspect of problem-solving
resolve a conflict — used when the problem involves disagreement between people or parties
figure out what went wrong — frequently used in analytical or reflective contexts
⚠️ Watch out
"Resolve" sits at the slightly more formal end of neutral register and can sound stiff in casual conversation if overused — in those moments, "figure out" is the better choice. Avoid using "figure out" in very formal documents such as legal writing or academic papers, where it may read as too casual.
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When the café's point-of-sale system stopped accepting card payments on a busy Saturday morning, the manager, Priya, resisted the urge to call the helpline immediately. Instead, she took ten minutes to figure out what had changed since the previous evening's update. She noticed a setting had toggled off automatically during the install. She fixed it herself in under two minutes. Later, a colleague asked how she stayed calm. "I've learned that most problems aren't as complicated as they feel," she said. "You just have to slow down enough to figure out what you're actually dealing with before you can resolve it properly."
The Quiet Art of Solving Problems Under Pressure
When journalist and author Cal Nguyen was researching his book on decision-making in high-stakes environments, he expected to find that the best problem-solvers were the fastest. What he discovered was almost the opposite.
The people who consistently performed well under pressure — emergency coordinators, experienced engineers, seasoned editors — shared one trait: they slowed down just enough to figure out the real nature of a problem before acting on it. Not for hours. Sometimes for just a few deliberate minutes. But that pause made an enormous difference.
"We tend to confuse urgency with clarity," Nguyen writes early in the book. "We feel pressure to move quickly, so we start solving before we truly understand what we're solving."
His research drew on interviews with over two hundred professionals across twelve industries. Again and again, the most effective individuals described a similar internal process: resisting the first obvious solution, asking one or two sharper questions, and then methodically working to resolve the actual issue rather than its surface symptoms.
Nguyen is careful not to present this as a personality trait. It is, he argues, a learnable habit — one that anyone willing to practice it can develop, regardless of industry, role, or experience level.
In professional contexts, 'determine / establish' means to analyse a situation carefully and arrive at a clear solution, answer, or course of action. It is used when a problem requires structured thinking and a definitive resolution.
Type
Transitive verb
Collocations
determine the cause — used when identifying the source of a problem or failure
establish a resolution — used when agreeing on or confirming a solution
determine the best approach — common in planning and strategy discussions
establish a course of action — formal phrase used in reports and meeting minutes
determine the extent of — used when assessing the scope or scale of an issue
⚠️ Watch out
Both 'determine' and 'establish' carry a formal, conclusive tone, so avoid using them in casual internal messages where they may sound overly bureaucratic. Note also that 'establish' can sometimes imply setting something up (e.g. establishing a team), so ensure context makes clear that you mean reaching a conclusion rather than creating something new.
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When a major client flagged inconsistencies in three consecutive invoices, account manager Priya Sharma knew she had to act quickly. She pulled together the billing records from the past quarter and worked closely with the finance team to determine exactly where the discrepancies had originated. It turned out that a data migration earlier in the year had caused certain rate codes to be incorrectly applied. Once the source was identified, Priya was able to establish a straightforward correction process. She documented the steps clearly, communicated the resolution to the client, and recommended a monthly reconciliation check to prevent the issue from resurfacing.
The merger between Calloway Group and Easton Partners had been anticipated for months, but the integration process proved far more complex than either leadership team had expected. Conflicting software systems, overlapping client accounts, and misaligned reporting structures had created a tangle of operational issues that no one had fully anticipated during the due diligence phase.
Chief Operating Officer Marcus Webb was brought in specifically to lead the integration taskforce. With a background in post-merger restructuring, he had seen similar situations before and understood that urgency without clarity only made things worse. His first move was to convene a cross-functional working group drawn from both organisations. Over the course of two intensive weeks, the group reviewed every flagged issue systematically.
By the end of the second week, the taskforce had managed to determine the primary sources of friction — three of which were immediately actionable without significant cost. The remaining issues required longer-term structural changes, but the path forward was now clear.
In his report to the board, Marcus outlined the findings and presented a phased integration roadmap. The board approved it unanimously. What had felt like an intractable situation had, with the right process, become manageable. Marcus often said that in his experience, organisations rarely lacked solutions — they simply lacked the discipline to establish them properly.
In academic English, 'ascertain' means to establish or determine something through careful investigation or analysis, while 'derive' means to obtain a conclusion, formula, or answer through systematic reasoning or calculation. Both serve as formal alternatives to the everyday phrasal verb 'work out' when describing the process of arriving at a solution through rigorous intellectual effort.
Type
Transitive verb (both 'ascertain' and 'derive' function as transitive verbs requiring a direct object, typically a noun phrase representing the conclusion, value, or solution obtained)
Collocations
ascertain the extent — used to determine the scope or magnitude of a phenomenon
ascertain whether — introduces an embedded question, common in empirical research writing
derive a formula / equation — standard in STEM disciplines when expressing mathematical problem-solving
derive conclusions / insights from — signals the source of reasoning in analytical writing
ascertain with certainty / confidence — collocates with epistemic adverbs to signal degree of evidential support
⚠️ Watch out
A common error is using 'derive' intransitively without a direct object (e.g. 'the results derived from the data' when 'were derived' is intended), which can create ambiguity about agency. Additionally, 'ascertain' should not be used in contexts where the process of discovery is ongoing or speculative — it implies a definitive determination has been reached, so avoid pairing it with hedging language such as 'may' or 'possibly'.
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Dr Adesanya had spent three weeks staring at conflicting datasets. Her colleagues had moved on to new projects, but she remained convinced that a coherent pattern existed within the noise. Working methodically through each variable, she eventually ascertained that the anomaly originated from a flawed calibration procedure used during the second data collection phase. Once the corrected values were reintegrated, she was able to derive a clean causal model — one that elegantly explained the discrepancy the team had dismissed as random error. She submitted her findings to the journal that same evening, quietly satisfied.
The question of how scientific consensus forms around contested empirical claims has occupied philosophers of science for decades. Thomas Kuhn's influential account of paradigm shifts offers one explanatory framework, yet it struggles to accommodate the incremental, negotiated character of consensus-building in contemporary large-scale collaborative research. In fields such as genomics or high-energy physics, where datasets are vast and methodologies are deeply specialised, the capacity of any single researcher to ascertain the validity of a given finding independently is severely constrained. Peer review, replication studies, and meta-analyses therefore serve not merely as quality control mechanisms, but as collective epistemic instruments through which communities of scholars derive shared conclusions from otherwise unmanageable evidential complexity.
This distributed model of knowledge validation raises important questions about accountability and interpretive authority. When no individual scientist can independently verify every inferential step in a multi-authored study, the notion of scientific objectivity must be reconceived as a property of communities rather than individuals. Emerging work in social epistemology suggests that institutional structures — including editorial policies, funding bodies, and data-sharing mandates — play a constitutive role in shaping what counts as a legitimate solution to a research problem. Understanding these structures is, therefore, not merely a sociological curiosity but a matter of profound epistemological significance.