Excellent explanation. What makes it so clear is that you "factor" the modified expression to show exactly why the 25 is in there. Most people don't include that part in the explanation. Understanding how and why is so much better than trying to memorise a series of stages that make no sense without context. Thank you.
Thank you so much!! I looked at like 5 different videos and none of them made any sense to me until this one!! All of the others just beat around the bush and did some weird method that took like ten minutes. I wished I could give 20 thumbs ups. You've got a new subscriber!
Great explanation! One thing I would add at the end. 32 is 16 * 2. Therefore, after the plus and minus we can put four times the square root of 2. That would be in a more simplified form.
THANK YOU! This helped me so much with studying for a test. No other video explained it like this and i was completely clueless. You explained it so well and made it so much easier to understand!!
You breaking it down is beautiful, thanks for the help. You're an angel! you didn't leave anything out and you answered ALL my questions thoroughly. sorry I'm 8 years late lol
My gods. I was so confounded as to why we were doing all that stuff to b in ax^2+bx+c=0. I don't know how i didn't recognize the perfect square before! Why do so many math courses insist on just telling you how to get the right answer without explaining how it works or what the underlying concept is?! It makes so much sense now. I'm ashamed for not realizing it all right away. I wish i could give this video more than one thumbs up. My gods...
twistedblktrekie I've been homeschooling myself alone with books and online resources for over a year now. The internet and myself are the best teachers i've ever had. Math teachers would practically never explain anything. I went to a public school in a ghetto too, so, that also probably didn't help. I can hardly wait until i start calculus. I never imagined that i would actually love mathematics.
twistedblktrekie I learn in a similar way, but for me, if it doesn't make sense to me conceptually, i'll have more trouble recalling it, and i'll get frustrated, so, i usually don't move on until i understand the concept adequately at the very least (by my own judgement i suppose, but hey). Luckily, the concepts often aren't difficult for me to understand at all, but i'm only on algebra 2 right now. I desperately want to be a physicist. I don't know if i can, or if i can even get into a good university due to my past and the circumstances my past has put me in. But it's what i want anyway. I'm 19, so i'm already very behind too.
twistedblktrekie My mom is a nurse; knowing what i know, i would never ever get into medical. Physics is my dream. It has been since 1st grade. I'm just not giving up because there isn't much else i want out of life aside from that anyway, aside from my dogs and some video games. Money doesn't matter much to me as long as i have those 3 things and sustenance, basically.
twistedblktrekie Honestly, i only took half a course in quantum mechanics before i decided to stop and go learn the math first. But, that half a course changed the world in my eyes, and i feel like it's something i'd like to put my life into. I loved physics since first grade; i just didn't know it before about a year and a half ago. There are a lot of good physics courses online, and a lot of good books if you're interested. I personally would recommend the Feynman lectures firstly. Wish me luck... I'll probably have a hard time getting into a good university, but, i suppose i'm too dense to give up.
twistedblktrekie It depends. There are jobs in universities, in companies, and for the government. The university jobs are the best; and the most difficult to attain. I do not want to work for the government, but company jobs can vary greatly. I want to be able to do actual research though. I really need to get into a top school, at least for grad school. People who go to just any old university for a physics major seem to always end up in a cubicle farm doing work that their heart isn't in.
Check out Mind Your Decision's explanation of quadratics using geometry. It visually shows "completing the square" making it concrete why you take half of b and square it. Really neat way to see it. This was still very good. Putting the two together is helpful.
could you do a video about rational functions, equations, and inequalities i'm having a hard time dealing with complicated problems but you're videos always helps out. thank you very much :)
This is the most rationale explanation I have seen. Moreover, the narrative can be said to be measured, natural and straight to the point. Impressive way of reassuring learners whilst going through the steps in a clear and humble manner. In short, the video is about the subject and not about 'creating a personality or show' to pseudo entertain. Love this method of calm step by step explanation.Could there be a similar video, but of the type where the x squared term has a leading co-efficient?
Great to hear, thanks man. No I don't have any videos specifically about that, but you can always divide both sides of the equation by whatever the leading coefficient is to eliminate it. If you proceed from there with the same method, it won't be pretty but it'll work. Cheers
@@user-in9of6os2c ... yes... you have to move the end coefficient to the other side in order to make a perfect square on one side... but also note you have to add the new coefficient to both sides in order for the equation to balance. As you can see, he’s not done anything that unbalances the equation. Eg, he hasn’t added to one side, that he hasn’t done for the other... I hope that helps. The formula he gave is ‘B (middle coefficient of x) divided by 2 and squared’. So, half of 10 and squared = 25... then add 25 to both sides. Also remember, X is one side of the equation and Y is the other... on your graph, you have X axis, positive & negative, and Y axis, positive and negative.... thus a squared graph, and why the expression is completing the square. After you’ve solved the quadratic equation, for X & Y, you can then plot or plug in the numbers onto your graph... it looks hard, but when you know how and why it’s used, it’s actually a work of genius.
THANK YOU. Geezus. I'm a grown adult taking a business math class, and I'd forgotten how to factor that out. After two days of watching videos and reading books, this finally clicked for me. Thank you thank you thank you.
Completing The Square really makes sense when you see it done with the area model. It because obvious why the middle term is divided in 2 and squared. A Quadratic is a square, geometrically-speaking. The reason you divide the middle term in 2 is because each side lengths have to be the same. You square it because you are literally adding a missing square units (length X width) to the larger square to make it whole. One thing I've learned about math is the more you understand (concepts and mathematical logic), the less you have to memorize. Math is just the language of numbers. Good luck in school.
They say a topic isn’t fully understand until the person can teach it, yep, this guy understands it, makes it look oh so simple 🙀🙀😳😩, is a really good video..
Thank you SO much. I am studying for my CSET and this is the only one that breaks it down the way that makes sense. I couldn't figure out what the point was in using Completing the Square when we can factor or use the Quadratic Equation. Other channels say "If a is equal to 1, add b/2 squared and it completely threw me off. But, what if a is not equal to 1?
OMGGGG THANK YOU IVE BEEN STUCK WITH THIS FOR 9HRS BUT NOW I UNDERSTAND GOD BLESS YOU I WAS ABOUT TO CHECK YOUR OTHER VIDEOS BUT YOU ONLY HAVE *VIDS WE NEED MORE PEOPLE LIKE YOUUUUUUU AAAA THANKASSASAS
@@stuartbowman_ Oh my gosh, I had thought you left, your tutoring level is so much better then anyone I find on youtube and they try to make it look cool with graphics but you doing it on paper really makes it feel like authentic maths! I wish you would come back
dude, thank you SO much! i was having a hard time with this and this totally helped! bonus points for also actually explaining how and why it works the way it does!
I can think of factors that multiply to give -7 and add to give 10: 5 + sqrt(32) 5 - sqrt(32) The point being, just cause something can't be factored using integers, it doesn't mean it can't be factored.
Thank you for taking the time to explain each step (even the "dumb" ones). Other videos we watched on this subject glossed over the "obvious" steps, making them impossible to follow (giving me flashbacks to some of the really bad math teachers I've had). My son was able to complete his math homework, thanks to you!
Thanks - very useful -- normally that '25' that you put in is put in as a fraction over 2, then brackets which are squared ... exactly the same thing, but o much more confusing when you don't really realise what's happening to/with that extra equation - this made it crystal clear :)
Acellus needs to hire you. My daughter is so frustrated with math. Im so frustrated with my attempts to help her. Would you be upset it i wrote/spoke with the school about you?
I'm looking at the comments in a bunch of videos and all these people seem like they are in a higher grade than me doing what I'm doing. I'm in 8th grade? What? I'm home schooled but someone pls answer my question. Why is this happening to me. Okay I'm done (btw u r better than my teacher)
Yes: sqrt(32)=sqrt(16*2)=sqrt(16)*sqrt(2)=4*sqrt(2). He probably left out the simplification so as not to distract from the main point of the video, but you make a good point.
