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Other forms: solved; solving; solves

To solve something is to find a solution, like figuring out the answer to a complex riddle.

The verb solve is often used in mathematics, and it means to answer a math problem. You can solve other, non-mathematical problems too — like the question of what to wear when you've run out of clean clothes (your sibling's clothes!). The word solve originally came from the Latin solvere , which meant "to loosen or untie." If you think of any kind of complex problem as a knot, then the original definition of solve still makes sense!

• verb find the solution to (a problem or question) or understand the meaning of “did you solve the problem?” synonyms: figure out , lick , puzzle out , work , work out see more see less types: show 7 types... hide 7 types... answer , resolve understand the meaning of riddle explain a riddle strike arrive at after reckoning, deliberating, and weighing guess , infer guess correctly; solve by guessing answer give the correct answer or solution to break find the solution or key to tell discern or comprehend type of: understand know and comprehend the nature or meaning of
• verb find the solution “ solve an equation” “ solve for x” synonyms: resolve see more see less types: factorise , factorize resolve (a polynomial) into factors type of: calculate , cipher , compute , cypher , figure , reckon , work out make a mathematical calculation or computation
• verb settle, as of a debt “ solve an old debt” synonyms: clear see more see less type of: determine , settle , square off , square up settle conclusively; come to terms

Vocabulary lists containing solve

A thorough survey of various textbooks, assignments, content area standards, and examinations yields the following list of words compiled by Jim Burke . You cannot expect to succeed on assignments if you do not understand the directions.

To improve your fluency in English Language Arts and Reading (ELAR), learn this academic vocabulary list that includes words selected from the Texas Essential Knowledge and Skills (TEKS) state standards.

Learn these words from the magazine article by Arlene Erlbach (Inside: Level B, Unit 1). Here are our links to the selections of "Imagine the Possibilities" : Hitching a Ride , Crittercam to the Rescue , LAFFF , Kids Are Inventors, Too , Inventing to Solve a Problem , The Evolution of a Great Idea Here are our links to the units of Level B: Unit 1 , Unit 2 , Unit 3 , Unit 4 , Unit 5 , Unit 6 , Unit 7 , Unit 8 Here are our links to the Inside books: Level A , Level B , Level C Here is our link to a list of academic vocabulary for Inside: Academic Vocabulary

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Synonyms for Solve problems

386 other terms for solve problems - words and phrases with similar meaning.

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Znaczenie słowa resolve w języku angielskim

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resolve verb ( SOLVE )

• The dispute over the song rights proved impossible to resolve.
• A mediator has been called in to resolve the crisis .
• They had an awful row several years ago, but now they've resolved their differences .
• The president is predisposed towards negotiation and favours a peaceful way of resolving the crisis .
• I'm sure these problems can be satisfactorily resolved.
• band-aid solution
• be at the bottom of something idiom
• break the deadlock
• clear (something) up
• heuristically
• holding operation
• iron something out
• surmountable
• talk something out

resolve verb ( DECIDE )

• decide I've decided to move to Sweden.
• fix UK The price has been fixed at £10.
• set Have you set a date for the wedding?
• finalize We've chosen a venue for the wedding, but we haven't finalized the details yet.
• settle OK then, we're going to Spain. That's settled.
• settle on/upon Have you settled on a place to live yet?
• promise I promise that I'll be home before dark.
• guarantee I can't guarantee that the operation will be successful.
• give (someone) your word He gave me his word that the job would be finished on time.
• assure "Don't worry, your car will be ready tomorrow", the mechanic assured him.
• swear I didn't know what happened, I swear.
• pledge We are asking people to pledge their support for our campaign.
• be make or break for someone/something idiom
• be on the horns of a dilemma idiom
• fish or cut bait idiom
• flip a coin idiom
• get something into your head idiom
• split decision
• swing the balance idiom
• take it into your head to do something idiom
• take the plunge idiom

resolve verb ( MUSIC )

• acciaccatura
• harmonic progression
• hemidemisemiquaver
• secco recitative

Czasownik frazowy

• perseverance A years-long political scandal broke last week thanks to the dogged perseverance of local reporters.
• determination After years of hard work and determination, she was finally promoted to CEO.
• persistence He was known for his persistence in the pursuit of justice.
• stick-to-it-iveness US This type of work requires a long-term commitment and a lot of stick-to-it-iveness.
• single-mindedness Her single-mindedness helped her win six US Open singles titles.
• doggedness Their sheer doggedness and ambition helped them ignore criticism and carry on.
• aggressiveness
• bloody-mindedness
• bull something through
• character-building
• insusceptible
• intransigence
• sharp elbows idiom
• sharpen (something) up
• sharpen your elbows idiom
• single-mindedness

resolve | American Dictionary

Resolve noun [u] ( decision ), resolve | business english, przykłady resolve, tłumaczenie resolve.

Uzyskaj szybkie, bezpłatne tłumaczenie!

a type of large tree that grows in northern areas of the world, or the wood of this tree

Fakes and forgeries (Things that are not what they seem to be)

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• Definicje Jasne wyjaśnienia naturalnego, mówionego i pisanego języka angielskiego. angielski Learner’s Dictionary Essential British English Essential American English
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• resolve (SOLVE)
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• resolve (DECISION)
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"problem" po polsku — Słownik angielsko-polski | zobacz "problem" po angielsku

Problem ***** , prob. (skrót).

• problem I think we've got a problem. (Myślę, że mamy problem.) There was only one problem. (Był tylko jeden problem.) It's the key to this problem. (To jest klucz do tego problemu.) zobacz także: dilemma , quandary , obstacle , difficulty
• zadanie We have to get down to this problem. (Musimy się zabrać za to zadanie.) Will you take care of this problem? (Zajmiesz się tym zadaniem?)
• zagadnienie [policzalny]

problem rzeczownik

Dodatkowe przykłady dopasowywane są do haseł w zautomatyzowany sposób - nie gwarantujemy ich poprawności.

If you have a problem with what I said, tell me.

Looking the other way will not make the problem go away.

But maybe the problems are not all in the feet.

She says if I have any problems ask the kids.

So what's the problem now if we want to help people?

She does not work because her back has a little problem .

If I want to take the day off, no problem .

People are getting themselves set up for some real problems .

Getting a late start is the least of the company's problems .

I can't help them when they have problems at school.

They want to know what to do about the problem .

I don't want to know just what the problems are.

I had no problem with what the president was saying.

They say the problem may start at the top of the department.

So, I would say take care of the problem now.

He wanted to know what to do about these problems .

These problems do play a role, according to the new study.

If they were doing their job, what was the problem ?

And both have already had major problems with the law.

How many people really want to read about their problems ?

In the end, I really have a problem with what he does.

We have economic problems in our country, and so do they.

All three were known to have had a heart problem .

I'm going to work out my problems and go on.

In the end, the show went off without major problems .

• problemowy (np. sztuka)

have a problem

• mieć problem I have a problem. Could you help me, please? (Mam problem. Czy mógłbyś mi pomóc, proszę?)

have a problem czasownik

But in the past I haven't had a problem with them.

If Tell had a problem , he would have said something.

Of course I have a problem with what you're doing.

Never had a problem in my life until a couple years back.

Often the first place you have a problem is your feet.

If you have a problem or need help, just ask.

Just answer the questions and you shouldn't have a problem .

He was always the guy to see when you had a problem .

The state has had a problem with it for years.

In the city, 47 percent said they would have a problem moving.

I have never met anyone who has had a problem doing the same thing.

I believe that 's a problem we need to cut off now.

If it goes beyond 7, you might be having a problem .

And that is something Green has never had a problem doing.

"No teacher has ever had a problem with what I have said."

You always have someone to talk to if there 's a problem .

I'm not one of those who had a problem with the whole thing.

Do I have a problem with you running the army?

"I understand you have a problem with one of our students."

For a second there, I thought you had a problem .

"Why ever would I have a problem with her being here?"

"Do any of you have a problem with working in trade?"

I had a problem with that a month or two ago.

Powiązane zwroty — "problem"

"problem" po angielsku — słownik polsko-angielski | zobacz "problem" po polsku.

• problem , sprawa , kwestia [policzalny lub niepoliczalny] It's none of your concern! (To nie twoja sprawa!) I would like to now focus on our first concern. (Chciałbym teraz się skupić na naszym pierwszym problemie.) You have to deal with it on your own, it's not my concern. (Musisz sam sobie z tym poradzić, to nie jest moja sprawa.)

• problem (z kimś , w jakiejś sytuacji) [policzalny lub niepoliczalny] I have trouble understanding fractions. (Mam problem ze zrozumieniem ułamków.) She causes a lot of trouble. (Ona powoduje dużo problemów.)

• udręka , problem [policzalny zwykle liczba mnoga] This is your trial, not mine. (To twój problem, nie mój.) Trials will end once you die. (Problemy skończą się, gdy umrzesz.)

• problem , kłopot [policzalny] We don't have many clouds. (Nie mamy wielu kłopotów.) Have you got a cloud? (Masz jakiś problem?) Don't worry, I'll help you with your cloud. (Nie martw się, pomogę ci z twoim kłopotem.)

• obciążenie , zawada , balast , problem , ciężar (np. o osobie, o rzeczy) [policzalny] He has become a serious liability to our business, and that cannot continue. (Stał się poważnym obciążeniem dla naszych interesów i nie możemy tego tolerować.) To znaczenie występuje najczęściej w pojedynczej postaci.

• wstyd , problem , kłopotliwa sytuacja , obciach (powód do wstydu) [policzalny] It's a major embarrassment, having an uncle in prison. (To straszny wstyd mieć wujka, który siedzi w więzieniu.)

• kłopot , strapienie , problem Our company is in financial straits. (Nasza firma ma kłopoty finansowe.) If you don't listen to me, you'll be in straits. (Jeśli mnie nie posłuchasz, będziesz miał kłopoty.)
• trudność , problem There's something wrong with your thought process. (Istnieje jakiś problem w twoim procesie myślowym.)

• problem , kłopot , niebezpieczeństwo , ryzyko Are you aware of the pitfalls maintaining your own company entails? (Czy zdajesz sobie sprawę z ryzyka, które jest wpisane w zarządzanie własną firmą?)

• problem , przeszkoda

• problem , zagwozdka There might be a little wrinkle with that. (Może być z tym mały problem.)
• problem , wrzód na dupie potocznie
• problem , trudna sytuacja

• problem , sprawa potocznie

• sytuacja , problem

• przeszkoda , problem   BrE potocznie

• kłopot , problem , trudność (skrót od słowa "problem") slang

• problem , szkopuł (coś, co denerwuje)
• trudność , problem [policzalny]

zmartwienie , niepokój , frasunek

czyjś problem

• czyjś pech , czyjś problem potocznie I don't care about that - it's your hard luck. (Nie obchodzi mnie to - to twój problem.)

mieć problem

• have a problem   I have a problem. Could you help me, please? (Mam problem. Czy mógłbyś mi pomóc, proszę?)
• be in a bit of bother  

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Meaning of "Solve over the reals?"

I am a bit confused about the wording presented in some radical equation problems I have been seeing.

The directions state simply to "solve over the reals"

Here is an example:

$$\sqrt{x^2-26}=\sqrt{x-6}.$$

By squaring both sides and solving the resulting quadratic we get $x=-4, x=5$. Clearly both of these solutions are real, but when we evaluate the original equation at these values we get equality of two complex numbers.

My question is: is this wording implying that our solutions $x$ need to be real values, or that they need to be in the domain of each side of each expression in the equation to cause equality in the reals.

My interpretation is that "solve over the reals" means the solutions need to be real, but I may be wrong on this. If this is what is implied, is there a concise wording that would imply the need for equality in the reals as well?

• complex-numbers
• real-numbers

• 3 $\begingroup$ You do not get $x=-4,5$ as solutions. The two expressions make sense when $x \geq 6$, so there are no real solutions. $\endgroup$ –  Gibbs Commented Jun 6, 2018 at 19:55
• 1 $\begingroup$ @fulltilt10: This is a good question. I would tend to interpret the phrase to mean that the equation is considered as an equation of real numbers, so your $x=-4,5$ solutions would be solutions over the complex numbers. A supporting piece of evidence is that the square root function is multi-valued over the complexes. There is no way to consistently pick the "positive" one, so if you write $\sqrt{x}$ you normally mean that $x$ is real and positive. Otherwise you have to "pick a branch." $\endgroup$ –  Cheerful Parsnip Commented Jun 6, 2018 at 20:01
• $\begingroup$ +1 for a possibly helpful teaching tip. The issue, of course (this remark is for others reading who know what's going on), has to do with extraneous solution , but your question shows that saying "solve over the reals" probably needs to be made more explicit when someone is first learning about it. $\endgroup$ –  Dave L. Renfro Commented Jun 6, 2018 at 20:02

2 Answers 2

Whenever you're told to solve an equation, you must always take into account the domains of the original equations.

Take for example the equation

$$\dfrac{x^2+5x+6}{x+2}=0\text{.}\tag{*}$$ Since division by zero is not valid, $x \neq -2$, but one could think to just multiply $x+2$ on both sides to get $$x^2 + 5x + 6 = 0$$ or $$(x+2)(x+3) = 0$$ yielding $x = -2$ or $x = -3$, but we must ignore $x = -2$ in this case, since it is not a solution to the original equation (*).

In your example, you are told to solve the equation $$\sqrt{x^2-26}=\sqrt{x-6}$$ over the real numbers.

The domain of $\sqrt{x-6}$ is $[6, \infty)$.

Now note $$\sqrt{x^2-26}=\sqrt{(x-\sqrt{26})(x+\sqrt{26})}$$ and since $\sqrt{\cdot}$ is only defined for nonnegative ($\geq 0$) values, it must be the case that one of two things must happen:

• Both $(x-\sqrt{26})\geq 0$ and $(x+\sqrt{26}) \geq 0$.
• Both $(x-\sqrt{26})\leq 0$ and $(x+\sqrt{26}) \leq 0$.

Suppose (1) happens. This means that $$x - \sqrt{26} \geq 0 \implies x \geq \sqrt{26}$$ and $$x + \sqrt{26} \geq 0 \implies x \geq -\sqrt{26}$$ or in short, $x \geq \sqrt{26}$ (note the "and;" where $x \geq \sqrt{26}$ is where BOTH $x \geq \sqrt{26}$ and $x \geq -\sqrt{26}$. You can also think of this as intersecting number lines).

Suppose (2) happens. This means that $$x - \sqrt{26} \leq 0 \implies x \leq \sqrt{26}$$ and $$x + \sqrt{26} \leq 0 \implies x \leq -\sqrt{26}$$ or in short, $x \leq -\sqrt{26}$.

Thus, it must be the case that $x \in (-\infty, -\sqrt{26}] \cup [\sqrt{26}, \infty)$.

The domains of the two equations on both sides are $[6, \infty)$ and $(-\infty, -\sqrt{26}] \cup [\sqrt{26}, \infty)$. Since $\sqrt{26} \approx 5.09 < 6$, we will only be looking at the intersection of these two domains, which would be $[6, \infty)$.

If I solved $$\sqrt{x^2-26}=\sqrt{x-6}$$ I obtain $$x^2-x-20 = (x-5)(x+4) = 0$$ which yields $x = 5$ and $x = -4$, but neither of these solutions are in $[6, \infty)$. Thus, there are no solutions.

It looks like your problem is on the definition of the square root. In general the square root is a map $\sqrt{\cdot }\colon [0,+\infty) \rightarrow [0,+\infty) $ such that $\sqrt{x} = y$ if and only if $y \geq 0$ and $y^2 = x$.

If your variable is real (resp. complex) and you allow values in $\mathbb{C}$, i.e. $\sqrt{\cdot}\colon \mathbb{R} \rightarrow \mathbb{C}$ (resp. $\sqrt{\cdot}\colon \mathbb{C} \rightarrow \mathbb{C}$) you are using a different definition of the square root operator. You should check what your definition is in your reference.

Suppose that the definition is the first one above. Define $f(x) := \sqrt{x^2-26}$ and $g(x) := \sqrt{x-6}$. Since the square root operator takes non-negative real numbers in input and returns non-negative real numbers, the functions $f$ and $g$ are defined when $$ \begin{cases} x^2-26 \geq 0 \\ x-6 \geq 6. \end{cases} \Rightarrow \begin{cases} x \leq -\sqrt{26} \text{ or } x \geq \sqrt{26} \\ x \geq 6. \end{cases} $$ The solution of this system is $x \geq 6$. Now, since the square root operator is also bijective, you have that $f(x) = g(x)$ if and only if $f(x)^2 = g(x)^2$, which implies $(x-5)(x+4)=0$. So $x=5$ or $x=-4$. Both these roots are less than $6$, so they are not really solutions of the equation. You end up with no real solutions.

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