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Homework Help: Completing the square

  1. Sep 3, 2010 #1
    y=7x^2-28x+3


    so far ive got...
    y-7(x^2-4x)+3
    then i divided 4/2=2
    and then did 2^2 = 4
    sooo
    y=7(x^2-4x+4-4)+3
    and thats as far as i can get
     
  2. jcsd
  3. Sep 3, 2010 #2

    HallsofIvy

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    You've done the hard work, now just use a(b+ c)= ab+ ac
    [itex]7(x^2- 4x+ 4- 4)+ 3= 7(x^2- 4x+ 4)+ 7(-4)+ 3[/itex]
     
  4. Sep 3, 2010 #3
    im supposed to end up in the form y=a(x-h)^2+k though
     
  5. Sep 3, 2010 #4
    The solution HallsofIvy gave does in fact end up in such a form. To find it, consider: what does [tex]x^2 - 4x + 4[/tex] equal? In other words, how can you get from [tex]x^2 - 4x + 4[/tex] to (x-h)^2? Similarly, you can get from [tex]7(-4) + 3[/tex] to k.
     
  6. Sep 3, 2010 #5
    did kind of trial and error and i guess it equals (x-2)^2
    but how do you actually figure that out?
     
  7. Sep 3, 2010 #6

    eumyang

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    You have to use the square of a binomial pattern:
    [tex](a - b)^2 = a^2 - 2ab + b^2[/tex].

    And ffter completing the square a number of times you'll start remembering the perfect square trinomials:
    [tex]x^2 - 2x + 1 = (x - 1)^2[/tex]
    [tex]x^2 - 4x + 4 = (x - 2)^2[/tex]
    [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]
    [tex]x^2 - 8x + 16 = (x - 4)^2[/tex]
    [tex]x^2 - 10x + 25 = (x - 5)^2[/tex]
    ... and so on.


    69
     
  8. Sep 3, 2010 #7
    ok sooo ive got y=7x^2-28x+3
    = 7(x^2-4x)+3
    =7(x^2-4x+4-4)+3
    =7[(x-2)^2-4)]+3
    =7(x-2)^2-28+3
    =7(x-2)^2-25

    so i thought that was the whole answer...
    but the answer in the book says the answer is 7[(x-2)^2-25/7]
    what did i do wrong?
     
  9. Sep 3, 2010 #8

    HallsofIvy

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    You did nothing wrong- but you seem to have forgotten your basic algebra:

    7a+ b= 7(a+ b/7) (distributive law)
     
  10. Sep 3, 2010 #9
    aahhh ok thanks to everyone!
     
  11. Sep 3, 2010 #10
    shoot...
    k im on the next one and its

    3x^2+3x+5
    soo i have =3(x^2+x)+5
    =3(x^2+x+.25-.25)+5

    but what do i do when its not a perfect square
     
  12. Sep 3, 2010 #11

    Dick

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    x^2+x+0.25 is a perfect square. It's (x+0.5)^2. Isn't it? You do exactly the same things you did before.
     
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