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Math Help - Completing the Square

  1. #1
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    Completing the Square

    Hey i am attempting to CTS 4x2 +24x-18=0

    i divide by four to make the a coefficient zero but then get lost at the 18/4 and dont know what do with that.

    Any help is appreciated
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    Re: Completing the Square

    you are trying to what... CTS?
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    Re: Completing the Square

    Ya i know the answer from the answer sheet but everytime i try i get the wrong answer.
    The answer is supposed to be x=1/2(-6 plus/minus 3 √6) bu this way seems like it was divided by two and the a coefficient was 2...
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  4. #4
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    Re: Completing the Square

    Quote Originally Posted by gramgilb View Post
    Ya i know the answer from the answer sheet but everytime i try i get the wrong answer.
    The answer is supposed to be x=1/2(-6 plus/minus 3 √6) bu this way seems like it was divided by two and the a coefficient was 2...

    Exapand (2x+6)^2-54 and see what you get.
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    Re: Completing the Square

    ya i got it ty
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    Re: Completing the Square

    Foe such questions adopt the folloing algorithm.
    Step - 1: Make coefficient = 1. in this case : divide by 4: x^2 + 6x - 9/2 = 0
    step - 2: transfer the constant term to the RHS: we will get x^2 + 6x = 9/2
    Step 3: Add the square of half the coefficient of x on both the sides of the equation. in this case the coefficient of x = 6; Half the coefficient of x = 3 and square of this is 9. Thus we have: x^2 + 6x + 9= 9/2 + 9
    That gives ( x + 3 )^2 = 27/2
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    Re: Completing the Square

    Quote Originally Posted by gramgilb View Post
    Hey i am attempting to CTS 4x2 +24x-18=0

    i divide by four to make the a coefficient zero but then get lost at the 18/4 and dont know what do with that.

    Any help is appreciated
    For this particular problem here is a possible approach.

     4x^2 + 24x = 18

    fnd  \sqrt{4} = 2 , now divide 24 by  (2 \sqrt{4}) = 4  ,  \frac{24}{4} = 6 , then square 6, 6^2 = 36

    now look where sqrt(4) = 2 , 6 and 36 go...

     (2x + 6)^2 - 36 = 18

     (2x + 6)^2 = 54

    The square has been completed... extract the roots...

     2x + 6 = \pm \sqrt{54}

     2x = -6 \pm 3 \sqrt{6}

     x = \frac{-6 \pm 3 \sqrt{6}}{2}

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  8. #8
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    Re: Completing the Square

    Quote Originally Posted by gramgilb View Post
    Hey i am attempting to CTS 4x2 +24x-18=0

    i divide by four to make the a coefficient zero but then get lost at the 18/4 and dont know what do with that.

    Any help is appreciated
    Using the standard method...

    \displaystyle \begin{align*} 4x^2 + 24x - 18 &= 0 \\ 4 \left( x^2 + 6x - \frac{9}{2} \right) &= 0 \\ 4 \left( x^2 + 6x + 3^2 - 3^2 - \frac{9}{2} \right) &= 0 \\ 4 \left[ \left( x + 3 \right) ^2 - 9 - \frac{9}{2} \right] &= 0 \\ 4 \left[ \left( x + 3 \right) ^2 - \frac{27}{2} \right] &= 0 \\ 4 \left( x + 3 \right) ^2 - 54 &= 0 \end{align*}

    Go from here...
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