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Math Help - Complete the Square

  1. #1
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    Complete the Square

    Complete the square for 3x^2 - 7x + 12 = 0

    MY WORK:

    I know that the coefficient of the x^2 term must be 1 in order to complete the square.

    I divided everything by 3 and came up with this:

    x^2 -(7x/3) + 4 = 0

    I then subtracted 4 from both sides and got this:

    x^2 - (7x/3) = -4

    I then took 1/2 of -7/3, which is 14/9, and squared that to add to both sides and got this:

    x^2 - (7x/3) + (196/81) = -4 + (196/81)

    Where do I go from there?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    Complete the square for 3x^2 - 7x + 12 = 0

    MY WORK:

    I know that the coefficient of the x^2 term must be 1 in order to complete the square.

    I divided everything by 3 and came up with this:

    x^2 -(7x/3) + 4 = 0

    I then subtracted 4 from both sides and got this:

    x^2 - (7x/3) = -4

    I then took 1/2 of -7/3, which is 14/9, and squared that to add to both sides and got this:

    x^2 - (7x/3) + (196/81) = -4 + (196/81)

    Where do I go from there?
    Don't subract 4 at that point. First complete the square at that point.

    \left(x+\frac{7}{6}\right)^2-\left(\frac{7}{6}\right)^2 + 4=0

    Then solve for x using algebra techniques.

    EDIT: You will get a complex answer.
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  3. #3
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    When completing the square, remember the general form. Then all you have to do is plug in your a, b, c.


    a\left(x+\frac{b}{2a}\right)^{2}+\underbrace{c-\frac{b^{2}}{4a}}_{\text{constant}}

    Take yours

    a=3, b=-7, c=12

    3\left(x+\frac{-7}{2(3)}\right)^{2}+12-\frac{(-7)^{2}}{4(3)}

    3\left(x-\frac{7}{6}\right)^{2}+\frac{95}{12}
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  4. #4
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    7/6....

    Quote Originally Posted by galactus View Post
    When completing the square, remember the general form. Then all you have to do is plug in your a, b, c.


    a\left(x+\frac{b}{2a}\right)^{2}+\underbrace{c-\frac{b^{2}}{4a}}_{\text{constant}}

    Take yours

    a=3, b=-7, c=12

    3\left(x+\frac{-7}{2(3)}\right)^{2}+12-\frac{(-7)^{2}}{4(3)}

    3\left(x-\frac{7}{6}\right)^{2}+\frac{95}{12}
    Where did the fraction 7/6 come from?
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  5. #5
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    Re :

    f(x)=3x^2-7x+12
    f(x)=3(x^2-7/3x+4)
    f(x)=3[(x-7/6)^2+4-(7/6)^2]

    Do you see now ?
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  6. #6
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    Quote Originally Posted by magentarita View Post
    Complete the square for 3x^2 - 7x + 12 = 0

    MY WORK:

    I know that the coefficient of the x^2 term must be 1 in order to complete the square.

    I divided everything by 3 and came up with this:

    x^2 -(7x/3) + 4 = 0

    I then subtracted 4 from both sides and got this:

    x^2 - (7x/3) = -4

    I then took 1/2 of -7/3, which is 14/9,

    1/2 of -7/3 is NOT 14/9, it is -7/6.

    and squared that to add to both sides and got this:

    x^2 - (7x/3) + (196/81) = -4 + (196/81)

    Where do I go from there?
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  7. #7
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    yes...

    Quote Originally Posted by mathaddict View Post
    f(x)=3x^2-7x+12
    f(x)=3(x^2-7/3x+4)
    f(x)=3[(x-7/6)^2+4-(7/6)^2]

    Do you see now ?
    Yes, I do....Thanks
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  8. #8
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    I see...

    Quote Originally Posted by HallsofIvy View Post
    1/2 of -7/3 is NOT 14/9, it is -7/6.
    I see what I did wrong.

    I divided -7/3 by 1/2 and got -14/9.

    I had to multiply -7/3 by 1/2 to get -7/6.

    I got it now. Thanks.
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  9. #9
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    Quote Originally Posted by magentarita View Post
    I see what I did wrong.

    I divided -7/3 by 1/2 and got -14/9.

    I had to multiply -7/3 by 1/2 to get -7/6.

    I got it now. Thanks.
    Note: - \frac{7}{3} \div \frac{1}{2} \neq -\frac{14}{9}.Rather, it's - \frac{14}{6}.
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  10. #10
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    Quote Originally Posted by mr fantastic View Post
    Note: - \frac{7}{3} \div \frac{1}{2} \neq -\frac{14}{9}.Rather, it's - \frac{14}{6}.
    Isn't it - \frac{14}{3}?
    Sorry was just flicking through the forum
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  11. #11
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    Quote Originally Posted by craig View Post
    Isn't it - \frac{14}{3}?
    Sorry was just flicking through the forum
    Well, on Earth it certainly is. But not on a backward planet named toidi, which is where I was visiting at the time.
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  12. #12
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    Quote Originally Posted by mr fantastic View Post
    Well, on Earth it certainly is. But not on a backward planet named toidi, which is where I was visiting at the time.
    Glad to see it happens to the best of us at times
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  13. #13
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    ok...

    -7/6 divided by 1/2 = -7/6 X 2/1 = -14/6

    I spend so much time with high school level math that primary school math now seems distant.
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