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 :)
@@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.
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.
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.
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
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.
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.
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.
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.
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 :)
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]
@@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).
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.
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!
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?
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😃
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.
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😃
You are very welcome Earl! I'm sure you are very smart 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
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?
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😃
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.
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
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👍👍
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 😃
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 .
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”.
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.
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😃
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.
On laptop/Computer you go to the RU-vid 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 RU-vid 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".
Thanks sir This is my dad's phone .My teacher taught me this 5 five but i was not understanding .but yoday i saw ur video , u are fabulous I understood very fast
You're very welcome Umesh! 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. Take care dear 😃
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
In China,Chinese students learn Quadratic equation of one variable at the age of 14,but some Chinese students learn it at age of 10,11. This equation can be solved by complete squareformula or formula method.
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.
