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28 May, 14:53

Solve the Quadratic Equation by factoring. 3r^2-16r-7=5

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  1. 28 May, 17:53
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    So first set one side to zero

    subtract 5 from both sides

    3r^2-16r-12=0

    factor

    to find the factor in

    ax^2+bx+c form when a>1

    multiply a and c together

    find what 2 numbers add up to b and multiply to ac so

    a=3

    b=-16

    c=-12

    ac=3 times - 12=-36

    factors that add up to - 16

    2 and - 18 is the answer since 2 times - 18=-36 and 2-18=-16 so

    split the middle number up

    3r^2-16r-12=0

    3r^2-18r+2r-12=0

    group

    (3r^2-18r) + (2r-12) = 0

    factor out common factors

    (3r) (r-6) + (2) (r-6) = 0

    reverse distribute (ab+ac=a (b+c) so

    (3r+2) (r-6) = 0

    set each to zero

    r-6=0

    add 6

    r=6

    3r+2=0

    subtract 2

    3r=-2

    divide 3

    r=-2/3

    r=6 or - 2/3
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