Algebra problem (Completing the square)!?

Discussion in 'The Okie Corral' started by Turtle13, Jan 14, 2010.

  1. Turtle13

    Turtle13 Ni!

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    I've got a decent hold on this crap finally. However, if you look at the picture my answer is wrong. My -1 should be positive. I understand where to make the change to make it right, I just don't understand why. Anyone brave enough to explain? I know that line 5 should read (x-1/2)^2 but why? I'm sure it has something to do with the form of the equation on line 4 (second and third coeff signs). If someone could point me to the rule or whatever I'm missing I'd be very pleased.
    [​IMG]
     
  2. Turtle13

    Turtle13 Ni!

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    Just a little background. When I took intermediate algebra they barely touched on completing the square. What problems they did have us do were nice and clear cut. Now I'm in Algebra II and the professor is treating completing the square like we're supposed to be veterans at it. He covered it for like 5 mins at the end of class and once again, nice clear cut problem. When you do the homework you run into much more complex stuff than was covered (read: fraction city).
     

  3. CitizenOfDreams

    CitizenOfDreams

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    (a+b)^2=a^2+b^2+2ab, not just a^2+b^2. As for "why?"... we were given an explanation in 4th grade, but it's been so long ago... :crying:
     
  4. Javelin

    Javelin Got Glock? Silver Member

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    8 years since that crap. So.... :dunno:

    :rofl:
     
  5. bob_fuller

    bob_fuller

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    i didn't even pay attention in class
     
  6. Turtle13

    Turtle13 Ni!

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    what you gave me doesn't prove what I'm seeing here. What you just typed would make my answer correct. I have the form (a+b)^2, my problem is that to get the right answer it should really be (a-b)^2.

    The actual answer is supposed to be 1+-i over 2. Not -1+-i over 2.

    In short, I almost have it right. One of my signs is wrong.

    There's a gap in teaching between these two courses and I'm really going to war with this crap to try and get a good grasp so I don't fail.
     
    Last edited: Jan 14, 2010
  7. bandmasterjf

    bandmasterjf

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    I took algebra II in 1985. It's not real fresh. :dunno:
     
  8. CitizenOfDreams

    CitizenOfDreams

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    Hmmm...

    Actually, the answer IS (-1+-i)/2, according to the quadratic formula:

    ax^2+bx+c=0;
    x=(-b+-SQRT(b^2-4ac))/2a.

    Entering the coefficients a, b, c into the quadratic formula...
    x=(-4+-SQRT(4^2-4*4*2))/2*4;
    x=(-4+-SQRT(16-32))/8;
    x=(-4+-SQRT(16)*SQRT(-1))/8;
    x=(-4+-4i)/8;
    x=(-1+-i)/2.

    Your line 5 is correct, I don't know why I thought you made a mistake there. Your answer appears to be correct as well.
     
  9. ryanm

    ryanm

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    It looks accurate to me as written. Your answer of (1+-i) over 2 would be right if the 2nd term was (-4x) instead of (+4x). Did the sign get miscopied when starting the problem?

    note: It has been several years since algebra!
     
  10. jetdefiant

    jetdefiant

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    based on my calculation the correct answer is
    (-1 (+/-)i)/2

    so what you have is fine
     
  11. Turtle13

    Turtle13 Ni!

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    Nope, I checked it against the one in the book several times out of paranioa! :crying:

    What's worse, I just did this problem and the signs worked out properly. It's almost the same format. I'll be pissed if the book is wrong.

    Check this one out.
    [​IMG]
     
  12. ryanm

    ryanm

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    It does sound like the book is wrong on that one
     
  13. Petrie

    Petrie

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    I dug out the old College algebra book and I just used the the equation for solving a quadratic equation (just plug in a,b, and c) and I got the answer you have written down on your paper. The solution to a quadratic equation starts with -b and since b is 4 in your specific equation I don't see how you could end up with a 1 and not a -1. I hate imaginary numbers:upeyes:.
     
  14. Turtle13

    Turtle13 Ni!

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    Then the book has to be wrong.
    Here it is in the back, note the answer to 49 as well, with its (-1)
    [​IMG]
     
  15. Turtle13

    Turtle13 Ni!

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    I would have just used quadratic if I had the choice but the point of the exercise was to complete the square. Which I hate. The understanding I'm starting to gain is actually making me hate it more.
     
  16. Petrie

    Petrie

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    piss on the book.:supergrin:
     
  17. CitizenOfDreams

    CitizenOfDreams

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    Life wouldn't be so exciting if textbooks had all the right answers. :supergrin:
     
  18. Nufrifin

    Nufrifin

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    Why would you do that?
    Do they force you to use that method?

    In quadratic equation ax^2+bx+c=0 roots x1 and x2 can be found

    x1=(-b+sqrt(b^2-4*a*c))/2*a
    x2=(-b-sqrt(b^2-4*a*c))/2*a
     
  19. Turtle13

    Turtle13 Ni!

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    Yes, the section calls for you to specifically do the operation by completing the square.
     
  20. jilverthor

    jilverthor

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    Agreed that the answer you have is correct. My guess would be that either:
    1. you copied the problem down wrong, easy to do
    2. the book was poorly printed, leading you to write down the wrong problem
    3. there was a typo in the book that leads the answers to be wrong (check online for an errata)


    ETR: Option 4, you identified the source of the answer
     
    Last edited: Jan 15, 2010