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Math Help - complete the square

  1. #1
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    complete the square

    i have a worked problem with solution, but need to check.

    3x^2+2x-8=0

    3x^2+2x=8

     <br />
x^2+\frac{2x}{3}=\frac{8}{3}<br />

    now i must take half coefficient of x and square,right?
    the next step i have been given is

     <br />
x^2+\frac{2x}{3}+\frac{1}{4}=\frac{8}{3}+\frac{1}{  4}<br />

    but i cannot see where the 1/4 is coming from?
    as 2x/3 divided by 1/2 = 1/3?

    thanks
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  2. #2
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    hello
    3x^2+2x-8=3\left ( x^2+\frac{2}{3}x-\frac{8}{3} \right )= 3\left (\left ( x+\frac{2}{6} \right )^2-\frac{4}{36}-\frac{8}{3}  \right ) =3\left ( (x+\frac{2}{6})^2-\frac{25}{9} \right ).
    u do some simplifications.
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  3. #3
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    hello okey so my step with 1/4 is wrong?
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  4. #4
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    Quote Originally Posted by decoy808 View Post
    hello okey so my step with 1/4 is wrong?
    looks that way.
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  5. #5
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    Quote Originally Posted by decoy808 View Post
    hello okey so my step with 1/4 is wrong?
    i don't see where 1/4 is coming from, but \frac{2}{3}x must be divided by 2 not \frac{1}{2}.
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  6. #6
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    haha do not trust computers
    my answer is x=2 or -4/3

    am i correct? many thanks
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  7. #7
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    Almost , x=-2 or x=\frac{4}{3}
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  8. #8
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    anyway, if the problem was "solve the equation",it would have been better if you factorized .
    3x^2+2x-5=(x+2)(3x-4)
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  9. #9
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    i take it back....garbage in, garbage out
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