Results 1 to 4 of 4

Thread: Completing The Square

  1. #1
    Join Date
    May 2008
    Posts
    1,345
    Mentioned
    0 Post(s)
    Quoted
    0 Post(s)

    Default Completing The Square

    Ok, I have to do a sheet on Completing the Square (didn't realize we had to hand it in, threw it out - gotta do it fast :P) with quadratic equations.

    The way we learned it went something like this:

    z^2 + 4z + 96 = 0.

    Make a new trinomial so it's a perfect square trinomial.

    (z^2 + 4z + (b/2)^2) + 96 = 0.

    So we get

    (z^2 + 4z + 4) + 96 = 0.

    Remove 96

    z^2 + 4z + 4 = 96.

    Factor

    (z + 2)^2 + 4 = 96

    Isolate the square

    (z + 2) ^2 = 100

    Square root it

    z + 2 = +/- 10

    Solve

    z + 2 = 10

    Subtract 2

    z = 8

    z + 2 = -10

    Subtract 2

    z = -12
    Which is all well and good.

    The book shows it done like this:

    Skip directly from z^2 + 4z + 96 = 0 to z^2 + 4z = 96

    z^2 + 4z = 96

    z^2 + 4z + (b/2)^2 = 96 + (b/2)^2

    z^2 + 4z + 4 = 96 + 4

    This is where my question comes up. In the next step, where the hell did the bolded + 4 go?!

    (z + 2)^2 = 100

    z + 2 = +/-10

    Solve in the same way I learned

    z = 8 and z = -12
    This second method the book shows seems nice, as it seems shorter. My problem is, where did that +4 go? How did they go about just... removing it?

  2. #2
    Join Date
    Feb 2009
    Location
    Irvine, CA
    Posts
    2,873
    Mentioned
    8 Post(s)
    Quoted
    138 Post(s)

    Default

    Is there anyway you can take a picture and upload it to imageshack or something? it's difficult to read with the ^ notation.

  3. #3
    Join Date
    Dec 2007
    Location
    192.168.1.73
    Posts
    2,439
    Mentioned
    6 Post(s)
    Quoted
    119 Post(s)

    Default

    z^2 + 4z + 4 = (z + 2)^2

    They just factorised it. So you end up getting z^2 (z*z), then 2 lots of 2z (2*z), then 4 ( 2*2)

  4. #4
    Join Date
    May 2008
    Posts
    1,345
    Mentioned
    0 Post(s)
    Quoted
    0 Post(s)

    Default

    Oh wow, I fail. I read (z + 2) ^ 2 = z^2 + 4z xD. Yeah, ok, I get it. Need to brush up on my FOIL apparently.

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •