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Math Help - completing the square

  1. #1
    Member princess_anna57's Avatar
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    Smile completing the square

    Solve by completing the square:

    x^2 - 3x + 2 = 0

    Please show step-by-step instructions because this is the first time I've come across this concept and I've looked through some examples but I can't determine the number that turns the left hand side of the equation into a perfect square?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    Solve by completing the square:

    x^2 - 3x + 2 = 0

    Please show step-by-step instructions because this is the first time I've come across this concept and I've looked through some examples but I can't determine the number that turns the left hand side of the equation into a perfect square?
    You know that
    x^2 + 2ax + a^2 = (x + a)^2
    right?

    So we want to find a way to put your equation into that form. The first step is to move the constant term to the other side of the equation:
    x^2 - 3x = -2

    Now, we want to add something to the left hand side to make it a perfect square. Look at that x^2 + 2ax + a^2 form again. If we can find what a is, then we need to simply add a^2. So look at the linear term, -3x in your case. We want to find a value for a, so set
    -3x = 2ax

    a = -\frac{3}{2}

    So we need to add
    a^2 = \left ( -\frac{3}{2} \right ) ^2 = \frac{9}{4}
    to the left hand side. But what we do to one side of the equation, we need to do to the other. Thus
    x^2 - 3x + \frac{9}{4} = -2 + \frac{9}{4}

    The left hand side is now in perfect square form. Simplifying the left and right hand sides gives:
    \left ( x - \frac{3}{2} \right ) ^2 = \frac{1}{4}

    Can you solve it from here?

    -Dan
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  3. #3
    Member princess_anna57's Avatar
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    my answers

    Is it:

    x - 3/2 = + square root 1 / 4 and x - 3/2 = - square root 1/4

    then

    x = 3/2 + square root 1 /4 and x = 3/2 - square root 1/4

    so x = 1.75 or x = 1.25
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    Is it:

    x - 3/2 = + square root 1 / 4 and x - 3/2 = - square root 1/4

    then

    x = 3/2 + square root 1 /4 and x = 3/2 - square root 1/4

    so x = 1.75 or x = 1.25
    no.. what is \sqrt{\frac{1}{4}}?
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by princess_anna57 View Post
    Is it:

    x - 3/2 = + square root 1 / 4 and x - 3/2 = - square root 1/4

    then

    x = 3/2 + square root 1 /4 and x = 3/2 - square root 1/4

    so x = 1.75 or x = 1.25
    x=\frac{3}{2}+\frac{1}{2}=2

    x=\frac{3}{2}-\frac{1}{2}= 1
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