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Math Help - complete the square

  1. #1
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    complete the square

    I know these are simple but these 2 are eating me up. I am having a real problem with complete the square when it envolves fractions for some reason. These 2 problems must be solved completing the square and please show me all the steps so that I can see where I have been messing up. Thanx
    X^2+7x+12=0
    2X^2+X-10=0
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  2. #2
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    Use the general formula and you won't have trouble.

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

    Enter in your values and you have it built. Try the first one: a=1, b=7, c=12
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by whiteowl View Post
    I know these are simple but these 2 are eating me up. I am having a real problem with complete the square when it envolves fractions for some reason. These 2 problems must be solved completing the square and please show me all the steps so that I can see where I have been messing up. Thanx
    X^2+7x+12=0
    2X^2+X-10=0
    1. x^2+7x+12=0

    Step1: Move +12 to right side of the equation.
    x^2+7x+ \;\;=-12+ \;\;

    Step 2: Take half the coefficient of x, square it, and add it to both sides.
    x^2+7x+\frac{49}{4}=-12+\frac{49}{4}

    Step 3: Left side is now a perfect square trinomial.
    (x+\frac{7}{2})^2=\frac{-48}{4}+\frac{49}{4}

    Step 4: Combine right side
    (x+\frac{7}{2})^2=\frac{1}{4}

    Step 5: Take square root of both sides.
    x+\frac{7}{2}=\pm \frac{1}{2}

    Step 6: Finish up.
    x+\frac{7}{2}=\frac{1}{2} \; \; or \; \; x+\frac{7}{2}=\frac{-1}{2}

    Step 7: Finally
    x=-3 \; \; or \; \; x=-4
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by whiteowl View Post
    I know these are simple but these 2 are eating me up. I am having a real problem with complete the square when it envolves fractions for some reason. These 2 problems must be solved completing the square and please show me all the steps so that I can see where I have been messing up. Thanx
    X^2+7x+12=0
    2X^2+X-10=0
    Take a look at Glactus' method. You might like it better.

    2. 2x^2+x-10=0

    Before you begin with the steps I showed you, you must make the coefficient of x^2 to be 1. Divide everything by 2.

    x^2+\frac{1}{2}x-5=0

    Step 1: Move -5 to right side of the equation.
    x^2+\frac{1}{2}+ \; \; =5+

    Step 2: See if you can finish the other steps.
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  5. #5
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    Thanx for the help. When you see it worked out it seems so simple. Thanx again
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