How do you work out 'completing the square'?

  • 0 votes

I just did completing the square in maths (GCSE unit 2 AQA) a few weeks ago but I've forgotten how to work it out (it's to do with algebra) please can someone tell me?? thanks :)

Posted Thu 12th April, 2012 @ 10:48 by :) PurpleJaguar (: - Team GR

4 Answers

  • 1 vote

general formulas are

x^2 +2bx +b62=(x+b)62

X^2 - 2bx+b^2 = (x-b)^2

its easier to remember

x^2+bx= (x+b/2)^2-(b/2)^2

so an example is x^2+ 8x=0

b=8 so

(x+4)^2 -4^2

=(x+4)^2 - 16

however sometimes we have -c as well for example

x^2 +8x+10 =0

so take the 10 to teh other side and forget about it for the moment

X^2+8x=-10

and as you see we've just doen that so we have

(x+4)^2-16=-10

bring teh 10 back over and you get

(x+4)^2 -6

if it asks you to work out x you do this

(x+4)^2=6

x+4=√6

x= -4 +/- √6

so x - -4-√6

or x=-4+√6 (but as i do alevel i don't know if  you need that if your confused just say and i'll try and break it down)

Answered Thu 12th April, 2012 @ 11:33 by bronwen :)
  • 1 vote

Well for completing the square you need to know how to work out answers for x which muddle earth1 has showed how to do.

What they might ask you is to convert a quadratic equation like " x^2 + 6x +15" into the completing the square or in the form (x+a)^2+b

IT MIGHT LOOK A BIT DIFFICULT BUT IT IS ACTUALLY QUITE EASY TO DO!!!!!

Lets take the equation I used earlier:

x^2 + 6x +15.......... and I want to put it in the form (x+a)^2+b where a and b are constants that need to be worked out.

To work convert in to completing the square you follow these simple steps!!!!!!!!!!

  1. Look at the coefficient of x (the number and sign in front of the x)
  2. Next you half that number and put that sign and number in the (x+a)^2 part
  3. Then you look at the number after without the x in the equation above
  4. After that the number you have in the (x+a)^2 ===> square that number and minus it (dont worry about the sign in the brackets just square that number and minus it out of the bracket).
  5. Now you can simplify outside the bracket and voila you have you completing the square.

Just to be sure ill do the example below!!!!!!!!!

  • x^2 + 6x +15 ====> So first half the number in front of the x ===> 6/2 = 3 
  • Put it in the (x+a)^2+b ==> (replace the "a" with your number)....... (x+3)^2+b
  • To workout the 'b' you square the number you worked out and minus it so its next to the bracket and then put the other number in the equation next to the bracket as well so you should get: ====> 3*3 = 9  ===> (x+3)^2 - 9 + 15
  • Now simplify and here is your answer!!! ==> (x+3)^2 - 9 + 15 ===> (x+3)^2 + 6

Hope I have helped!!!!!!!!!!!!!!!!!!!!!!!!!!!!   =)

Answered Thu 12th April, 2012 @ 15:00 by Braniac
  • 1 vote

x² + 6x – 7 = 0

x² + 6x = 7

6/2 = 3      6 + 3 = 9

(x + 3)² - = 7

(x + 3)²= 7 + 9

(x + 3)²16

= sqrt (16) 

x + 3 = 4    or    x + 3 = -4

x = 4 - 3    or     x = -4 - 3

x = 1         or     x = -7

Answered Thu 12th April, 2012 @ 15:15 by Dementia
Edited by Dementia on Thu 12th April, 2012 @ 15:21
  • 0 votes

Thanks guys for your answers I kind of remember how to do it now :):) thanks loads :D ***

Answered Thu 12th April, 2012 @ 19:30 by :) PurpleJaguar (: - Team GR
Edited by :) PurpleJaguar (: - Team GR on Thu 12th April, 2012 @ 19:32