Can you solve this Quadratic Equation by Completing the Square?

Learn how to solve quadratic equations by Completing the Square Method, a step-by-step tutorial. PreMath.com

[@giftyasare3602]

My daughter is using this mathematics to solve her assignment Thanks for your help and support.

[@PreMath]

You're very welcome Gifty Asare! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)

[@hemanthsai5486]

Good . But what Is the meaning of each step . Why we add the steps that we wanted , there should be some meaning right

[@Niteshsir]

Plz watch m.kzbin.info

[@xsageonexx7399]

@@PreMath Why do you: A. Pull the 7/6 aside and B. Divide it by 2?

[@lordkelvin100thompson8]

@@xsageonexx7399 Take, for example; x + b Square it: (x + b)(x + b), and carry out the multiplication to get the product: x^2 + 2bx + b^2 In the example polynomial, the 7/6 coefficient is your 2b, so you need to divide by 2, or multiply by 1/2 to get the value of b to add to the L-value to produce a perfect square.

[@ffggddss]

Or, in order to keep everything in integers for as long as possible, note that the middle coefficient is odd, so multiply by 4·6 (rather than by 6): 4·6·6x² - 24·7x = -24·8 12²x² - 2·12·7x = -192 12²x² - 2·12·7x + 7² = 49 - 192 (12x - 7)² = -143 x = (7 ± i√143)/12 Fred

[@alicedeanhera898]

0

[@BigWailz_official]

ffggddss :thanks so much sir,your explanation is so clear

[@basharathussain7212]

Genius

[@CentaurisNomadus]

Now i got the point of denoting quadratic root of negative numbers. Thank you.

[@vikg3228]

Dumb question maybe but half of 2nd coefficient is 84, so don’t follow how you’re getting to 7squared instead of 84squared? Trying to relearn basic math to help my kids :). Thx.

[@GillesF31]

I'm French. I'm retired (after a professional career in data processing). I love mathematics (it doesn't mean I'm an expert of it :-) and I APPRECIATE A LOT your videos. Thanks to them we can approach a high level of problem resolutions as this one in which the irrational number i is used to get the solution. Congratulation and thank you for sharing with us your high level knowledge.

[@Hertog_von_Berkshire]

9:16 When used as an operator, ± should be spoken as "plus or minus". "positive or negative" is correct only when ± is used as a sign.

[@CentaurisNomadus]

Yeah, contexts. Our teacher from math would note that, just like in your comment.

[@pillai21]

6x^2-7x+8 =0, a= 6, b = -7, c = 8, -b = 7, b^2 = 49, 4ac = 4×6×8 = 192, b^2 -4ac = 48-192 = - 144 < 0 Since it is negative , this equation has no real roots.

[@dmitrychaschev5489]

Именно так, и квадрат числа не может быть отрицательным, какой же тупой автор видео

[@ottolicha3213]

For me it is very funny how you calculate the right side of the equation. You could do it like this: -4/3 + 49/144 = -192/144 + 49/144 = -143/144. Your way to do it seems like if a mountain hiker wants to reach the height of 1000 meters, so he goes up to 5000 meters and then comes down.

[@vairnvain]

Same thoughts! I'm really bothered with how he added the fractions 😂

[@tintinfan007]

Exactly.....

[@breintankx]

Hello, I think you could also use: 1) D= b Square - 4ac Knowing D is your discriminant! 2) - b + square root of D = x1 3) - b - square root of D = x2 What do you think?

[@PreMath]

Thank you so much King for your nice feedback. You are perfectly alright about the discriminant D= b Square - 4ac. I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃

[@ianmoseley9910]

you must answer the question as written

[@someone3285]

D= -

[@amramjose]

Very well explained! Would using the quadratic formula result in the same answers?

[@alzakiruyaqub123]

Wonderful! Can we always take the half of coefficient number by 1\2...? And also can we also directly write the number obtained when multiplied by the coefficient number without making it smaller?

[@alzakiruyaqub123]

I mean can we always multiply the coefficient number by 1\2

[@dannyasio8614]

Excellent presentation. Thank you for this. I am now clarified that in finding a certain number to complete a square, we can possibly arrived on an imaginary number (ì). Kudos! Well explained.

[@PreMath]

You're very welcome Danny! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)

[@jihanjiji1]

Good professor 🌷💐🌺🌺💐

[@PreMath]

Thanks and welcome

[@dennisphilip7596]

Please make a video on real life use of limits , mathematical induction,complex numbers

[@themanagementwarrior]

Hi. What lecture app and/or tablet did you use in your online lecture? Thanks.

[@scottspartan9]

Why did you divide 7/6 by 2? Please clarify.

[@andywright8803]

Solving with the equation is much simpler A=6, b=-7, c=8 X=(7+/-sqrt(49-4×6×8))/12 =(7+/-sqrt(49-192))/12 =7+/-sqrt(-143))/12 =7/12+/-sqrt(143)i/12

[@lastchance8142]

Thank you. This is correct

[@BigWailz_official]

Please can you break down the simplification process so I can understand

[@andywright8803]

@@BigWailz_official the solutions to ax^2 + bx + c = (-b +/- sqrt(b^2 - 4ac))/ 2a. This seems quite complicated, but once you use it a couple of times, you find that unless factorisation is very simple, it's the simplest method, and I always find it simpler than completing the square. It works all the time and you can also tell very simply how many real solutions there are based on whether the value in the square root is positive (2), zero (1) or negative (0).

[@truthseeker-777]

Andy Wright that might be so, but the whole point of the video was to show that the completing the square method could be used - as his student had asked him. It does also bring in the concept of the imaginary number rather nicely and also builds on knowledge of splitting number to root them which is convenient too, for building in and reinforcing concepts covered in earlier lessons.

[@Ayushiteacher]

You explain very well👍

[@jeffrey3306]

Can you explain pls how and why are you dividing 7/6 by 2...where did you get that 2

[@breintankx]

I don't know why he does that but you could also use: 1) D= b Square - 4ac 2) - b + square root of D = x1 3) - b - square root of D = x2

[@3dbadboy1]

Can you bring the answer all over 12 (because of common denominators) or does the inclusion of 'i' not make that possible? (7 + i(143)² ) / 12 and (7 - i(143)² ) / 12 .

[@javierleon4895]

Good!! Tell me what software do you use to write??

[@PreMath]

Hello dear, we use Camtasia TechSmith package. Thanks for asking. Take care and stay blessed😃

[@woni9834]

Why can’t I use the method you taught, by doing (6x+1)(6x-8) and x = -1/6, or x _ 4/3?

[@handrianoperwira2626]

(6x-1)(6x+8) isnt equal to 6x²-7x+8

[@patrickguillory7552]

Anyone teaching equation should explain the rules........ Whenever someone understands the rules, everything becomes easy.

[@chessandmathguy]

The rules?

[@mikefrey6668]

Pure bs dreamt up by some arab this shit is out dated

[@kalyanbasak6494]

X=1.876,-0.71 answer sharing, thanks sir,is it correct?

[@henrydavis8910]

Yes I can but why should I when using the quadratic formula is so much easier?

[@PreMath]

Dear Henry, you are absolutely correct! However, getting to know more tools and techniques would give you more power! I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃

[@ianmoseley9910]

The question asked specifically for this method - in an exam you would lose marks for ignoring that

[@lordkelvin100thompson8]

The quadratic formula is a generalized form of completing the square. Good to know that because I'm always forgetting the damn formula.

[@johnnolen8338]

The quadratic formula is the result of CTS. If you become proficient at CTS then you'll not only know where the quadratic formula came from, the quadratic formula becomes completely unnecessary. CTS is faster.

[@joelb9378]

In germany we have something that's called pq-Formel: when you see this equation x^2 + qx + q = 0, you can do this: X = - p/2 +/- Squarerootof [ (p/2)^2 - q]

[@MichaelRothwell1]

May I suggest that when you combined the fractions, it would have been preferable to use the lowest common denominator, 144, rather than cross-multiplying, as this would lead to easier arithmetic with smaller numbers and avoid the need to cancel by sqrt(3) later.

[@stelun56]

Completing the square for this expression would be much better than beginning with the equation, as this also derives the coordinates for the vertex. If only roots are needed, then the formula is the obvious choice. Moreover, you should review adding fractions. -4/3 + 7^2/12^2 = -43/12^2. Only beauty lies in true mathematics.

[@PreMath]

Thanks dear for the nice feedback. I really appreciate that. Take care dear and all the best😃 Have a very happy and blessed New Year!

[@sonydeep5912]

Why to fill c ( notation a, b and c) was b divided 2, where was 2 come from?

[@larrypatterson3957]

Since they have a common denominator, would you further simplify the solution as x = (7+i[143]^1/2)/12 and (7-i[143]^1/2)/12 ? Also, thank you for taking the time to show us this method. You have a very easy method of teaching that helps me to understand the material.

[@PreMath]

Dear Larry Patterson , you are absolutely correct. You may simplify it further. As a Math professor, I'd accept both versions of answers as perfectly alright. Thanks for the feedback. I'll be uploading many more video lessons pretty soon. Kind regards

[@JamesMiller-rb3eo]

Larry Patterson hi

[@chadwickmeyer7844]

Larry. I did this problem with my algebra class and then we watched the video together. Like you, we further simplified the final answer.

[@everythinguwant4722]

Thank you so much for your explanation. I'm from India 🇮🇳but I can understand your explanation comletely.👍

[@PreMath]

You are very welcome Patel ji! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃

[@paulmiller6647]

This is so relaxing to the brain I feel loads just got lifted off my shoulders. I love getting a refresher on this; thanks very much for the link. It's been at least two years since I last did these equations.

[@mustafasleiman257]

You kan simply solve it with (X= -b + and - √b squar - 4ac all over 2a, a as 6 ,b as -7 ,c as 8

[@ReversePrimeOFFICIAL]

Mustafa Sleiman that’s not fun

[@truthseeker-777]

That’s not what his student asked him to do.

[@husseinelgandy6242]

We can ×6# 36 x^2_42x+48=0 then (6x_7/2)^2=_47/2

[@beartalon]

3 is a factor of 144. You only needed to multiply -4/3 by 48/48 and then add with 144 denominator. You could have saved steps there

[@sk__gauravpatil8334]

So best and great video but l am daily using video wow amazing sir l like you video

[@احمدالسويداوي]

What is the program used to explain the lesson please reply

[@PreMath]

Dear Ahmed, if you are talking about the software program, I use Camtasia Techsmith! All the best :)

[@DoctorFashion]

Subscribed! Great explanation!

[@PreMath]

Thank you so much! Please keep supporting my channel. Kind regards 😀

[@michaelkaye4998]

I’m long out of math. Like these videos to refresh my mind. What is the purpose of completing the square? Knowing the formula I would never bother with this. Is their a reason to?

[@damnson1356]

hahaahahahahahaha great question. well i guess teachers want us to fail, thats why

[@archeopterixneuroza4715]

it can help with maximums

[@jihanjiji1]

Good thanks

[@PreMath]

Thank you too!

[@sofab1549]

question. Why do u need to flip over the 2 over 1?

[@hichamroka9428]

Good explication. Thanks

[@aparnapatil72]

Sir how to solve this equation by factorization

[@sachinpai2886]

You cannot take Square root of an expression. It has to be in simplified form. Else it should be in Modulus.

[@prakasamkannadi7616]

Step by step approach to answer is simply super.

[@PreMath]

Thank you so much prakasam kannadi for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃

[@leopoldkudzaishungudzemoyo5597]

If we save the video to watch later how do we access it

[@PreMath]

Click on save beside like, dislike, share button and select watch later checkbox. Thanks for asking. Take care :)

[@theobserver314]

On laptop/Computer you go to the KZbin home page or simply put it www.youtube.com, then on your left side a column would appear, this column contains the following: "Home" "Trending" "Subscriptions" "Library" "History" "Your Videos" "Purchases" "Watch Later" "Show More" Click "Watch Later". If you're using mobile, upon opening the KZbin App there will be a row at the bottom that will contain the following: "Home" "Explore" "Subscriptions" "Inbox" "Library" Click "Library" Upon clicking "Library" You will than find "Watch Later".

[@karnabudhathoki5311]

@ around 4:10 you put (7/12)^2 On both sides. later you said what sign to put in between x and 7/12 whole square... It wasnt necessary...you simply should have said...its taking on the form of a^2 - 2ab+b^2. And will so...reduce to (a-b) ^ 2 .That way it would have been simpler....

[@NileshKumar-yj4sb]

Explanation was very good. You please shutup

[@theobserver314]

You are correct.

[@artmiller2341]

With two sheep flying, one yellow and the other heading right, how much does a pound of asphalt cost, given that the cow is 10 years old?

[@GlossRabban]

It costs the taste of musik made from star dust.

[@artmiller2341]

@@GlossRabban lol

[@gajavelliprincesses]

I don't understand why you have muliplied 7/6 with 2.

[@寧靜致遠-h1r]

If ax2+bx+c =0, the solution of formula is -b+-✓ b2-4ac（radical symbol)/2a.

[@cc-ic7rj]

Exactly right

[@karimelsheikh3296]

What is the name of boared please ??

[@Glockperfection666]

This is to help me refreshing for my daughter’s pre calculus . Thank you very much !!!!

[@shathaomar1516]

Why did you take the number 7/6 and multiply or divided it by half n then put exponents 2?? Could not get this step plz

[@rajakambing]

7x/12+7x/12=14X/12=7x/6

[@HDitzzDH]

Shatha Omar He’s doing that so that we can write the left side as a perfect square, that’s one of the main steps regarding how to solve by ”completing the square”.

[@djganit]

Very good presentation

[@PreMath]

Thanks a lot :)

[@raeesuddin5660]

Can we multiply and divide the coefficient of x by 2 ?

[@senpailegacy1583]

I knew immediately that they were imaginary because the nature of the root (or the discriminatnt I.e. b^(2)-4ac) is less than zero so it must mean it has two imaginary solutions. Great video👍👍

[@luisportella1760]

hahaha who cares fucking knowitall hahaha

[@vasilismagdabanos2542]

Gauss.

[@GurdeepSingh-yu4pt]

lol

[@HDitzzDH]

luis portella You can’t comprehend such low level math? Hahaha.

[@stormstrike1845]

What happened to the -7/6x?

[@kishalayamukherjee4867]

Great video for learners like us. But perhaps you forgot to tell the learners when you used the formula (a - b)^2 = a^2 - 2ab + b^2 in the LHS equation : x^2 - 7/6.x+ (7/12)^2 = ( x - 7/12 )^2. Instead, you brought down the negative sign before 7/12 by drawing an arrow. This confused me a little in the first hand. Thanks.

[@bhadra65]

Exactly! I had the same confusion for a little while, too.

[@mkwazir]

Amazing Good Well done Thank u sir

[@adelekeolabiyi6095]

Thank you so much I was able to challenge some people

[@mshahkhan9178]

need more explanation because why should we take square of 7/2. There is logic behind and this logic should be explain. good effort

[@e10ln]

Could you tell me please what is the name of that programe you are using it for writing ?

[@PreMath]

Camtasia! Thanks for asking. Kind regards :)

[@profbenchahyd8776]

please how to creat a matematics videos

[@PreMath]

Dear Hassan, I use CamtasiaTechSmith utility for my videos. Take care😃

[@profbenchahyd8776]

@@PreMath Thank you so much

[@PreMath]

@@profbenchahyd8776 My pleasure 😃

[@truthseeker-777]

When I was first looking at completing the square quadratics a few weeks ago, I stumbled across this video and it nearly blew my mind. I’ve studied a bit since and just rewatched it and bingo! Makes glorious sense now. Thank you 😊 But if you are a beginner to completing the square, start with a simple few examples that don’t involve fractions, to build your understanding first.

[@PreMath]

You are very welcome Lottie Bronte! Glad I could help you. Thanks for your comments. Please keep supporting my channel. Take care😃

[@manojsurya1005]

Can I just use quadratic formula?

[@PreMath]

Sure, you can! I used the completing the square method because my student requested me that method. Thanks for asking. Take care dear and all the best 😃

[@manojsurya1005]

@@PreMath thank u

[@philippemichel4330]

Yes it’s simpler.

[@carultch]

@@manojsurya1005 Completing the square is how the quadratic formula is derived in the first place. If all you are given in a problem, is to find the roots of the quadratic equation, you can use any method that is most convenient for you. If you are specifically told to use a particular method in the problem statement, you use that method.

[@josegeonzon3595]

Sir can you answer this one, f(x) = x^2+3x+2 by completing the square

[@PreMath]

Dear Jose Geonzon, here is the solution: solve by completing the square x^2+3x+2 = 0 => x^2+3x = -2 => x^2+3x +(3/2)^2= -2 +(3/2)^2 => (x + 3/2)^2 = -2 + 9/4 => (x + 3/2)^2 = 1/4 => take the square root on both sides and solve for x => x=-1, x=-2 are our solutions :) Thus, you can write your function f(x) = x^2+3x+2 as in this form as well => f(x) = (x + 3/2)^2 - 1/4. Thanks for asking. All the best :)

[@محمدحسن-ح6ث5ق]

Thank you for all this great knowledge

[@motherof3pearls]

When completing the square, why do some KZbin Math teachers add the middle terms on the left hand side and to the right hand sides, while others minus the term they have just squared on the left hand side. You get two different answers, right. I just so confounded by which method to use. Please, help! Thank you 😃🤓

[@shamskhan9891]

You can use any method

[@openyard]

I am a bit lost at 7:34, how did the square root of 429 become represented as square root of 3.143 and the square root of 423 become equal to the square root of 3.144?

[@jeffweber8244]

429 = 3 x 143 the dot was multiplication symbol, not a decimal point

[@numeshmani2183]

Divide:(12x^4-15x^3)÷3x^2 please

[@Hertog_von_Berkshire]

1:28 "The next thing what we want to do" ... I'm so glad this isn't an English lesson ... "isn't it".

[@kevinvu9802]

Can you tell me which software you are using?

[@PreMath]

Camtasia :)

[@kevinvu9802]

thanks

[@RealSlopeDude]

Great video. As a math teacher myself, I love how you skipped no steps.

[@PreMath]

MathGives YouPower , thanks for the honest feedback. We both are in this very noble teaching profession. Kind regards :)

[@domjervis]

Love the You Tube name you use. Reminds me of one of my favorite Adages. "Math is a Wonderful Thing. Become good enough at it, and no one will EVER be able to fool you with demagoguery." As for this video, my 8th grade algebra teacher took us through a drill very similar to this one. I raised my hand and asked "Wouldn't it be easier to just apply the Quadratic Equation?" He replied "With an attitude like that, you'd be better off becoming an Accountant than a Mathematician." So I did LOL All best!

[@leslieanderson6413]

where did the 7/12 and 2/1 come from? I think I have frozen my brain. I love math; this has me stumped. I would make my dad, the math prof so proud :)

[@jihanjiji1]

Good

[@PreMath]

Thank you so much! Please keep supporting my channel. Kind regards 😀

[@jihanjiji1]

@@PreMath ok my frand

[@learnmathsezy1]

Nice explanation. which application r u used thanks

[@PreMath]

Thanks vinesh rathod for the feedback. Kind regards :)

[@alejandroortiz4223]

Very clear to me as a student... Tnx

[@PreMath]

You are very welcome Oordnajela Zitro ! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends.Take care dear and all the best😃

[@hilurisetemekila505]

How can you get =+or - I square root 3.143

[@johnniegilkerson4724]

@5:39 in video (-429/432) reduces to -(143/144)

[@josefc8362]

johnnie gilkerson hahaha, exactly

[@FatimaZahra-on4po]

Sir i rude amount I don't understand where from we get

[@gaBetibu]

Hi, thank you for your kind, helpful explanation, but I didn't understand why you divide the 2nd term (b term) by 2? Thank you, again . . . & God Bless . . .

[@gaBetibu]

. . . oops, never mind, Sir . . . I just found the answer in one of your other super-great videos . . . Thank you so, so much, &, God Bless . . . :)

[@PreMath]

Dear Glo Amador, you are very welcome. Thank you so much for taking the time to leave this comment. I'm sure you are an awesome student. Keep it up. Best regards :)

[@joeblainey2627]

what software is used for writing on the youtube board

[@MathsclassKI]

Good question

[@PreMath]

Camtasia! Thanks for asking. Kind regards :)

[@johnbell3166]

u cross multiply fractions? I thought u find like denominator and add the fractions? (-4/3+49/144)?

[@TeWee.]

Im limited on my math. But why not split to binorminals and solve?

[@channelsixtysix066]

In electronic engineering, " i " is replaced with " j ". The reason for that is, lower case " i " is the current symbol in AC circuits.

[@rahinatufuseinu1662]

So....please,why did you divide 7/6 by 2?

[@vikramanvel]

Why don't you keep the captions what you talk on one side so that the steps by steps solution is not hidden.?

[@cobra4883]

how do you get sqrt3.143 equal to sqrt3 x sqrt143.

[@swkit125]

Where?

[@umamaheswari7446]

L.C.M.of 3 and 144 is 144 so -4x48+ 49 gives -143/144

[@kabonline09]

very good explanation... you are really good teacher and not for duffers like some of those who commented below....

[@amadoumbayediouf]

How to solve this equation please! 3 cos5x-4sin5x=3? I am Senegalese and l follow you great teacher Pape thanks you

[@karnabudhathoki5311]

I left teaching 7 years ago ..so I cannot give you solution right away..but I can give you ideas....since you dont have direct formulas for 5x but you do have formulas for 2x and 3x..so I think replacing 5x with 2x+3x is the right way to go...also there may be ( A-B) or ( A+B) formula scenarios....hope that helps...you ...Thanks...Nepal....

[@HDitzzDH]

Amadou Mbaye Diouf I think that problem is incredibly difficult, I looked up the answer and it was: x = 2/5( π*n - arctan(4/3)), x = (2πn)/5, n ∈ ℤ.

[@RobertoEmilioRomero]

Use the substitution sin(5x)=sqrt(1-cos^2(5x)). With some algebra together with the quadratic formula you should be able to solve. It you want the actual solution send me an email with the problem at [e-mail] Best,

[@drmadhan76]

Great sir.Thank you so much👍👏

[@anjaneyasharma322]

6x^2 - 7x = --8 6x(x--7) = --8 Choose the right one from 1 x --8 --1 x 8 2 x --4 --2 x 4 and find value of X

[@PreMath]

Thanks Anjaneya for your awesome feedback! Please keep sharing my channel with your family and friends. Take care dear and all the best😃

[@marcosreal11]

The steps would have been easier if you had just multiplied -4/3 by 48/48 (to get the 48, divide 144 by 3). Then if you are weak at fractions you could multiply both sides of the equation by 144.

[@rohankhtrapal7889]

I was also thinking the same

[@vasundharakarant2357]

At the beginning only you can use the formula as x=(-b±√(b^2-4ac))/2a

[@hacker64xfn99]

There is a : x² 1x = (x - ½)² - 1²/4 that is pretty easier ..

[@johnvinton6993]

Thanks to Po-Shen Lo (www.poshenloh.com/quadraticdetail/) the following is another elegant solution : If you find r and s with sum −B and product C, then x2+Bx+C=(x−r)(x−s), and they are all the roots • Two numbers sum to −B when they are −B/2±u • Their product is C when B2/4−u2=C • Square root always gives valid u • Thus −B/2±u work as r and s, and are all the roots So for the equation 6x2 - 7x + 8 = 0, we follow the following steps: Divide both sides by 6 resulting in x2 - 7/6x + 4/3 Two numbers that Sum to 7/6 are 7/12±u The product of the two numbers is (7/12 + u)(7/12-u)=4/3 Solving for you u as follows: 49/144-7u/12+7u/12-u2 = 4/3 49/144-u2 = 4/3 = 192/144 -u2 = 192/144 - 49/144 = 143/144 u2 = -143/144 u = (±i√143)/12 X = 7/12 (±i√143)/12

[@bismaali622]

Just subscribed ! You are a life saver

[@PreMath]

So nice of you Bisma dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃

[@peterbyrne6394]

Thank you.

[@PreMath]

You're welcome!

[@mathsfamily6766]

Pretty good sir! Best explainer

[@PreMath]

Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards

[@sadhsarkar1323]

Thank you.... thank you soooo very much sir......I was facing prblm in this thing for many days.... Thanks for clearing my doubt.........😊

[@ReligiousReasoning]

144 and 3 have a lower common multiple 144

[@garyleather6486]

Mate this good can you tell me where would you use this in life i am not trying to be a smartarse can someone explain it to me

[@MathsclassKI]

Very very good Very nice Super super