Math Is Fun Forum

thefishyispink

Member

Registered: 2008-05-19

Posts: 2

Completing the square problems =/

The question is:

3x² - 24x + 47

and for the life of me, I can't get the right answer:
3 ( x - 4 )² - 1

I can get the x - 4 part no problem, but am having difficulty getting any of my numbers to add to minus one, no matter what process I go through! Could somebody please help me by showing me the working to end up with -1?

Thank-you in advance!

Last edited by thefishyispink (2008-05-19 06:08:12)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Completing the square problems =/

if you expand the left part of it:

3(x-4)² = 3(x²-8x+16) = 3x²-24x+48

so how do you get from that to 3x²-24x+47, you have to subtract 1.

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thefishyispink

Member

Registered: 2008-05-19

Posts: 2

Re: Completing the square problems =/

Thanks!

Could I just ask, though - how would I do it using a method like the one on this page: http://www.mathsisfun.com/algebra/completing-square.html

This is the method I have been using, you see, and so I would really love it if somebody could explain it so that I could find out where my error is - I need to be able to do these questions!!

Thanks again!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Completing the square problems =/

The examples on that page are slightly different because they use equations, where here you've got an expression. It's not much different though, the only thing that's done in the equation that involves both sides is to bring the constant term to the other side for a bit and then put it back when you're finished. You can use pretty much exactly the same method here:

You start with 3x² - 24x + 47

Factor out a 3 to get a single x²:
3(x² - 8x + 47/3)

Complete the square:
3[(x-4)² - 16 + 47/3]

Simplify:
3[(x-4)² -1/3]

Simplify more:
3(x-4)² -1.

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thefishyispink

Member

Registered: 2008-05-19

Posts: 2

Re: Completing the square problems =/

Thanks very much for doing that! I get where I went wrong now. You're a star!