you have no idea how hard I looked for a maths channel that used this method. I kept finding American videos and it was really stressful. Thank you so much!!!
These videos are a massive help, started my A level maths course just a few weeks ago and wanted to go back over this topic. One question - in the example -5x2 + 20x - 9, why do you get ((x-2)2 -4) instead of +4 because if you’re squaring -2, wouldn’t you get plus 4 ? Or am I thinking incorrectly? Just confused me a bit. Thanks again
@@TLMaths yes yes of course. I have watched too many of your videos for today. My brain can no longer properly function. Thank you for the quick response, also I just wanted to say a big thank you for these amazing videos, and I just found out about your website, where all relevant information is very organised. So, I will be heading over there to study. Again, thanks for your time and effort!
You can write 8 - 3 as -3 + 8. So 8 - 3x - 2x^2 can just be re-ordered into 8 - 2x^2 - 3x or -2x^2 + 8 - 3x or -2x^2 - 3x + 8. You can't just change the sign of one of the terms, otherwise it changes the expression you're working with.
Are you planning on uploading the compete further maths A level too? If so, when do you think you’d be able to finish that? Thanks so much for all you do!
That will be my eventual plan, but it's been very difficult to fit in making videos of late due to other commitments at work. There is no end date for that yet - the full A-Level Maths videos took a year and a half to complete
Do you mean the step from -2(x^2 + (3/2)x) + 8 to -2((x + 3/4)^2 - 9/16) + 8 ? This is correct as I have completed the square on x^2 + (3/2)x inside the bracket, which is (x + 3/4)^2 - 9/16. www.wolframalpha.com/input/?i=complete+the+square+8-3x-2x%5E2
Dude listen. In the last question we gotta divide 3/2 by 2. That should turn to a 3. But u are getting a 3/4. My teacher told me to always divide the coefficienrt of x by 2
I'm not sure what I've done wrong. Some1 help me. 8 - 3x -2x² = 0 can be rewritten as 2x² + 3x -8 = 0. Then you solve this to 2(x+3/4x)² +73/8. I don't have the 'negative' before the two but can't find My mistake. What have i done wrong?
![A-Level Maths: B3-12 [Quadratics: Examples of Finding the Line of Symmetry]](http://i.ytimg.com/vi/iLx5P_ZLyAY/mqdefault.jpg)
![A-Level Maths: B3-12 [Quadratics: Examples of Finding the Line of Symmetry]](/img/tr.png)
![A-Level Maths: B3-23 [Quadratics: Solving More Complicated Equations Using Quadratic Methods]](http://i.ytimg.com/vi/84c100TyemU/mqdefault.jpg)
I can't believe that you have made over 1000 videos for us in this playlist!
you have no idea how hard I looked for a maths channel that used this method. I kept finding American videos and it was really stressful. Thank you so much!!!
Many American teachers teach it the same way he did here. I, however, use a slightly different approach.
You've provided an abundance of examples which are very similar in trickiness to ones in my textbook. Thank you for putting this out and helping us!
These videos are a massive help, started my A level maths course just a few weeks ago and wanted to go back over this topic. One question - in the example -5x2 + 20x - 9, why do you get ((x-2)2 -4) instead of +4 because if you’re squaring -2, wouldn’t you get plus 4 ? Or am I thinking incorrectly? Just confused me a bit. Thanks again
When you complete the square, you always subtract.
So for example:
x^2 + 6x - 1 = (x + 3)^2 - 9 - 1 = (x + 3)^2 - 10
x^2 - 6x - 1 = (x - 3)^2 - 9 - 1 = (x - 3)^2 - 10
TLMaths Thank you, this makes a lot of sense now. I appreciate it
Thank you so much for this! I struggled to get my head round this method and your explanations were very clear and helpful!!
You're very welcome!
Thanks alot this help me immensely keep up the good work 👍
Thank you for your hardwork man!
You are a life saver
Thank you so much this really helped me understand completing the square
good job my friend the way you completed these equations was just exhilarating
THE 🐐
thankyou, ur a legend
Excellent video sir good job
Than you So much
Hi, what if you can’t factor out the coefficient from the first two terms, for example: 2x^2 + 3x + 6
How would I solve this?
Please reply
You CAN factor the coefficient out from the first two terms:
2(x^2 + (3/2)*x) + 6
On the last question, how did you re arrange the equation?
Do you mean how do you get from
8 - 3x - 2x^2
to
- 2x^2 - 3x + 8 ?
@@TLMaths Yes.
It's just rearranging the terms like 3 - 2 is the same as - 2 + 3 ?
@@TLMaths yes yes of course. I have watched too many of your videos for today. My brain can no longer properly function. Thank you for the quick response, also I just wanted to say a big thank you for these amazing videos, and I just found out about your website, where all relevant information is very organised. So, I will be heading over there to study. Again, thanks for your time and effort!
No worries - don't forget to get some rest!
For Eq7 I didn't get how you changed the order of the equation without changing the - and + signs? Shouldn't -2x^2 become a positive 2?
You can write 8 - 3 as -3 + 8.
So 8 - 3x - 2x^2 can just be re-ordered into 8 - 2x^2 - 3x or -2x^2 + 8 - 3x or -2x^2 - 3x + 8. You can't just change the sign of one of the terms, otherwise it changes the expression you're working with.
Cheers mate
Are you planning on uploading the compete further maths A level too? If so, when do you think you’d be able to finish that? Thanks so much for all you do!
That will be my eventual plan, but it's been very difficult to fit in making videos of late due to other commitments at work. There is no end date for that yet - the full A-Level Maths videos took a year and a half to complete
@@TLMaths Do you think you will have Further Maths videos uploaded for September 2020? I really appreciate your work.
I don't know I'm afraid - I'm not working to any written-down schedule :-(
@@TLMaths hey i think there is a mistake on the last question as you changed 3/2 to 3/4 at the end
Do you mean the step from -2(x^2 + (3/2)x) + 8 to -2((x + 3/4)^2 - 9/16) + 8 ? This is correct as I have completed the square on x^2 + (3/2)x inside the bracket, which is (x + 3/4)^2 - 9/16.
www.wolframalpha.com/input/?i=complete+the+square+8-3x-2x%5E2
What if there’s no middle term? Like if you have -x^2+25 ?
-x^2 + 25 is already in completed square form
Hi, what if you had a question like 3x^2 - 2x ?
3x^2 - 2x
= 3(x^2 - (2/3)*x)
= 3((x - (1/3))^2 - 1/9)
= 3(x - (1/3))^2 - 1/3
@@TLMaths thank you so much, you’re a lifesaver! And does the 1/3 come from the 1/9 simplified?
Yes, from expanding the bracket
In last question why did you divide 3 by 2?
Pls reply!!
- 2x^2 - 3x + 8
Then I factored the -2 out of the first two terms:
-2 ( x^2 + (3/2)x ) + 8
TLMaths thanks!! So we always have to do this step whenever the coefficient of X is a negative term?
It's the same if the coefficient of x^2 is not 1
e.g.
2x^2 - 3x + 8
becomes
2 ( x^2 - (3/2)x ) + 8
Ok thankyou very much!!
question 6 -2 times -2 is 4 not -4
You ALWAYS subtract the square.
e.g.
x^2 + 6x + 5 = (x + 3)^2 - 9 + 5 = (x + 3)^2 - 4
or
x^2 - 6x + 5 = (x - 3)^2 - 9 + 5 = (x - 3)^2 - 4
Dude listen. In the last question we gotta divide 3/2 by 2. That should turn to a 3. But u are getting a 3/4. My teacher told me to always divide the coefficienrt of x by 2
Dude listen. 3/2 divided by 2 IS 3/4.
1.5 divided by 2 is 0.75, which is 3/4.
@@TLMaths 😂 I love that reply
Do you have a video of actually solving the equation by completing the square?
Yes here: ruclips.net/video/b1ycDKgDnmI/видео.html
I'm not sure what I've done wrong. Some1 help me. 8 - 3x -2x² = 0 can be rewritten as 2x² + 3x -8 = 0. Then you solve this to 2(x+3/4x)² +73/8. I don't have the 'negative' before the two but can't find My mistake. What have i done wrong?
8 - 3x - 2x^2 = 0
2x^2 + 3x - 8 = 0
2(x^2 + 3x/2) - 8 = 0
2((x + 3/4)^2 - 9/16) - 8 = 0
2(x + 3/2)^2 - 9/8 - 8 = 0
2(x + 3/2)^2 - 73/8 = 0
what if the question says its equal to y?
Doesn't make any difference?
y = x^2 + 2x + 8
y = (x + 1)^2 - 1 + 8
y = (x + 1)^2 + 7