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completing the square when the coefficient of x is not 1

Hi, i'm just doing a C1 past paper for my resit in Jan.

The question is express 4x^2 - 24x + 27 in the form a(x-b)^2 + c

the answer is 4(x-3)^2 - 9.. im just not sure how they managed to get -9 ? I understand the rest. The mark scheme doesnt really make it clear :s-smilie:

Thanks in advance.

Reply 1

Glutamic Acid

17

4x^2 - 24x + 27 = 4[x^2 - 6x] + 27 = 4[(x-3)^2 - 9] + 27 ...

Reply 2

Swayum

18

Different people do it different ways. I think the easiest way (and this is the way I do it) is to just factorise the coefficient of x^2:

4x^2 - 24x + 27
= 4(x^2 - 6x + 27/4)

And then just complete the square in the brackets. You can then rearrange it to any form they want it in quite easily (e.g. a(x - b) + c).

Reply 3

skatealexia

14

4 ( x^2 - 6x ) + 27

4 ( [ x-3] ^2 - 9 ) + 27

4 ( x-3)^2 - 36 + 27

4 ( x-3) ^2 -9

Reply 4

skatealexia

14

Glutamic Acid

You didn't multiply -9 by 4.

I noticed, thanks :smile:

Reply 5

Willis123

dont forget to -3^2

or as i like to say, minus 3 square-izzled.

Reply 6

darkraver

10

4x^2 - 24x + 27

Take out common factor, 4.

4(x^2 - 6x + 27/4)
4((x - 3)^2 + c)

Find c: We have (x - 3)^2 = x^2 - 6x + 9
So our current c = 9 or 36/4, but the old c was 27/4, so the new c must be -9/4

So: 4((x - 3)^2 - 9/4)
Simplifies to: 4(x - 3)^2 - 9

Reply 7

Nattynoo101

OP

Ooh, thanks a lot everyone, i think i get it now :smile:

much more helpful than trying to google it, all of the websites i found were useless!!

Reply 8

skatealexia

14

Nattynoo101

Ooh, thanks a lot everyone, i think i get it now :smile:

much more helpful than trying to google it, all of the websites i found were useless!!

I always try to ask on TSR =P

Reply 9

GoldieStocks

5

how about:
4x^2 - 24x + 27
=(2x-6)^2 -9

edit: sorry realised this isn't very useful

here you go:
4x^2 - 24x + 27
=(2x-6)^2 -36 +27
=(2x-6)^2 -9
=(2(x-3))^2 -9
=4(x-3)^2 -9

Reply 10

nombo

13

Ooo help me too please! I'm doing my Add Maths and I can't dolve this by completing the square:
2x^2 + 2x - 9
Or
2x^2 - 8x + 5
But since I have the same prob, you can just help on one. I just don't know what to do when the coefficient isn't 1...?

Reply 11

McLH

Original post by nombo

Ooo help me too please! I'm doing my Add Maths and I can't dolve this by completing the square:
2x^2 + 2x - 9
Or
2x^2 - 8x + 5
But since I have the same prob, you can just help on one. I just don't know what to do when the coefficient isn't 1...?

a(x+b)^2-d

=

a[(x+b)^2 -b^2]+c

(edited 12 years ago)

Reply 12

steve2005

17

Original post by nombo

Ooo help me too please! I'm doing my Add Maths and I can't dolve this by completing the square:
2x^2 + 2x - 9
Or
2x^2 - 8x + 5
But since I have the same prob, you can just help on one. I just don't know what to do when the coefficient isn't 1...?