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Completing the square

  1. Feb 23, 2004 #1

    Math Is Hard

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    Hello,
    I was working on a lengthy problem and got stuck on something simple. I have a quadratic expression 4(x^2) - 4x + 3 that I should have been able to complete the square on to rewrite as (2x - 1)^2 + 2
    My knowledge of applying this technique when a coefficient is attached to the leading term is rusty so I got out my old algebra books. The solution they offered was to set 4(x^2) - 4x + 3 = 0
    and then divide each side by four. With the coefficient removed, then the square can be completed the usual way. But this isn't giving me what I need at all.
    Any advice on this technique?

    Thanks mucho!!
     
  2. jcsd
  3. Feb 23, 2004 #2

    Tom Mattson

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    When you set aside the quadratic and linear terms, you can factor by grouping as in the following example:

    3x2-12x+2
    (3x2-12x)+2
    3(x2-4x)+2

    Note that I have factored the 3 out of the first two terms only. Now, I complete the square inside the parenteses.

    3(x2-4x+4)+2-12

    Note the parts in red. I added 4 to the expression in parentheses, but that 4 was multiplied by 3 to make 12. So, to keep the expression equal to my original expression, I subtract 12 (not 4) from it.

    Finally, I factor the perfect square in parentheses and collect terms.

    3(x-2)2-10

    edit: typo
     
  4. Feb 23, 2004 #3

    Math Is Hard

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    Thanks, Tom. Glad to see you are still on the homework help boards.
     
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