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Math Help - Help again

  1. #1
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    Help again

    Please explain how to solve this.

    The product of two consecutive even integers is 168. Find the two integers.
    Hint: Assume the first integer is x
    Set up the equation first that satisfies the given condition. Then solve the equation.


    This is the equation that i came up with. Ican t seem to get past

    x(x+2)=168

    x^2+2x-168=0 (i cant get past here)


    Thanks,
    Chester
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  2. #2
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    Quote Originally Posted by Chester

    x(x+2)=168

    x^2+2x-168=0 (i cant get past here)
    Good job.
    Find some factors of 168: 12 and 14
    which diffrence is 2 thus,
    (x+14)(x-12)=168
    Thus,
    x=-14,x=12
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  3. #3
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    You could always fall back on the quadratic formula. I'd rather factor.

    What 2 numbers when added equal 2 and when multiplied equal -168.

    Let's see.......how about.....................-12 and 14. (-12)(14)=-168

    -12+14=2

    x^{2}-12x+14x-168

    (x^{2}-12x)+(14x-168)

    x(x-12)+14(x-12)

    (x-12)(x+14)
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  4. #4
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    Hello, Chester!

    You did an excellent on job on the hard part: setting up the equation.
    So where is your difficulty?

    I assume you know to solve a quadratic equation
    . . and that you know how to factor.
    Did you run of factorings to try?

    x^2+2x-168\:=\:0

    We want two numbers with a product of 168 and a difference of 2.


    Start dividing 168 by 1, 2, 3, . . .

    168 \div 1 = 168\quad\Rightarrow\quad 1\cdot168

    168 \div 2 = 84\quad\Rightarrow\quad 2\cdot84

    168 \div 3\;\;\text{  not exact}

    168 \div 4 = 42\quad\Rightarrow\quad 4\cdot42

    168 \div 5,\; 168 \div 6,\;\168 \div 7\;\;\text{   not exact}

    168 \div 8 = 21\quad\Rightarrow\quad 8\cdot21

    168 \div 9,\;168 \div 9,\;168\div 10,\;168\div11\;\;\text{ not exact}

    168 \div 12 = 14\quad\Rightarrow\quad 12\cdot14\;\;\leftarrow There! a difference of 2


    Therefore: . x^2 + 2x - 168 \;= \;(x - 12)(x + 14)

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Of course, you can use the Quadratic Formula for factoring . . .

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  5. #5
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    Thanks

    Thanks again everyone.

    I really appreciate the help!

    Chester
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  6. #6
    MHF Contributor Quick's Avatar
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    I believe the answer is 12\cdot14 not (-12)\cdot14
    notice that negative 12 and 14 are not consecutive even integers.
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  7. #7
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    Quote Originally Posted by Quick
    I believe the answer is 12\cdot14 not (-12)\cdot14
    notice that negative 12 and 14 are not consecutive even integers.
    There two answers for x.
    x=12, x+2=14 and 12\times 14=168
    And,
    x=-14,x+2=-12 and -14\times -12=168
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