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Express x^2 - 10x in the form (x+p)^2 + q

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Express x^2 - 10x in the form (x+p)^2 + q

    State the value of P and Q

    3. The attempt at a solution

    I don't know! I don't get it because when I times out the brackets p will always be a number, and there are no numbers that aren't multiplied by x in x squared minus 10 x. Gragh?
     
  2. jcsd
  3. Feb 5, 2012 #2

    Curious3141

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    Homework Helper

    Expand this out: (x+p)^2 + q

    Compare the coefficients of this expression to x^2 - 10x (the constant term here is zero, i.e. the expression can be written x^2 - 10x + 0). What equations can you set up to define p and q?
     
  4. Feb 5, 2012 #3

    eumyang

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  5. Feb 5, 2012 #4
    Ok so I complete the square because i'm more comfortable with that:

    x^2 - 10x + 0 = 0

    x^2 - 10x = 0

    x^2 - 5^2 = 5^2

    (x-5)^2 - 25

    this would mean p = 5 and q = -25?

    This doesn't seem right? Have I gone wrong somewhere?
     
    Last edited: Feb 5, 2012
  6. Feb 5, 2012 #5
    It should be right as you wrote:
    x2-10x <=> (x+p)(x+p) + q <=> x2+2xp+p2+q.
    x2-5x-5x+25-25 <=> x2-10x

    p=5, q=-25
     
  7. Feb 5, 2012 #6
    p=-5 q=-25

    I find it quicker to half the x term.... so theres your p straight away -5

    and then sqaure p so -5^2 = 25 and you need +0 so its -25...

    another example is
    x^2 - 6x + 30

    so again half -6 is p= -3
    then again square -3 = 9
    and i need 30 so 9+21 q =21
     
  8. Feb 5, 2012 #7
    Cheers all, got the marks! :)
     
  9. Feb 5, 2012 #8

    Mark44

    Staff: Mentor

    Some quibbles:
    You're not working with an equation - just an expression.
    Didn't notice earlier, but this isn't correct.
    Where did the -10x term go? And how is it that you can add -5^2 to one side of an equation, but add +5^2 to the other. The answer is, you can't do this.
    Starting at the beginning, you have
    x2 - 10x
    = x2 - 10x + 25 - 25
    = (x - 5)2 - 25
    = (x + (-5))2 + (-25)
    I leave it for you to figure out what p and q are.
    Gliese123, Do not connect expressions with an equivalent sign. Expressions that are equal should be connected with =. Statements such as equations or inequalities can in some cases be connected with the equivalent symbol, <=>.
     
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