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Algebra: How does [-x^2 -4x+4-1] become [(x^2+4x-4)-1]

  1. Aug 31, 2013 #1
    If I want to complete the square with

    [itex](-x^{2}-4x+3)[/itex] I would write

    [itex](-x^{2}-4x+(...) +3 - (...)) = (-x^{2}-4x+4+3-4) = (-x^{2}-4x+4-1) = (x^{2}+4x-4) - 1[/itex]


    Why does adding the parentheses to separate the -1 change all the signs. I understand it has something to do with factoring out a negative, but how exactly?

    I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus?
     
    Last edited: Aug 31, 2013
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  3. Aug 31, 2013 #2

    arildno

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    "I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus? "

    It doesn't; you are perfectly correct concerning addition/subtraction relative to the associative property.

    The last expression is missing a minus sign in front of the parenthesis expression containing the completed square.
     
  4. Aug 31, 2013 #3
    -(x^2+4x-4)+7 ?
     
  5. Sep 1, 2013 #4

    verty

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    There's a mistake, x^2 + 4x - 4 is not a square.

    The correct way to start is:

    -x^2 - 4x + 3
    -(x^2 + 4x) + 3
     
  6. Sep 1, 2013 #5
    I'm confused as heck, but this is good practice since this is exactly what we're reviewing in math right now.

    If you start with -(x^2+4x) + 3, you divide that 4 by two and square it, resulting in -(x^2+4x+4)+3.

    However, you have do add that 4 to the outside, but doesn't the negative in the very front make it a negative 4, finally resulting in -(x^2+4x+4) + 7? I'm confused on where to go from here.
     
  7. Sep 2, 2013 #6

    verty

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    You have done the hard work, you just need to write it in the neatest way possible. Remember you want to have something like (x+a)^2.

    Here is a more abstract example for you to practice the steps on:

    x^2 + px + q = 0
     
  8. Sep 2, 2013 #7
    Think I got it:

    -(x+2)^2 + 7? :)
     
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