Algebra question!!?

What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0."

THANK YOU!!!!!!

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  • 1 decade ago
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    the third way is completing the square:

    12x^2 - 10x = 42,

    so

    x^2 - 5/6 x = 42/12 = 21/6

    cut the 5/6 in half to get 5/12, and add (5/12)^2 to both sides.

    x^2 - 5/6 x + 25/144 = 21/6 + 25/144

    The left side collapses into

    (x - 5/12)^2, and 7/6 + 25/144 = (584 + 25)/144 = 529/144

    so

    (x - 5/12)^2 = 529/144

    x - 5/12 = +/- sqrt(529/144) = +/- 23/12

    x= 5/12 + 23/12 = 28/12 = 7/3 or x = 5/12 - 23/12 = -18/12 = -3/2.

  • 1 decade ago

    "12x2 - 10x - 42 = 0."

    Technique one: factoring...

    Technique two: the quadratic equation

    Technique three: Simplifying the equation first (a 2 can be divided out before you continue)

  • 1 decade ago

    well theres factoring, like (6x -4)(2x+12)=0

    andd quadratic equation; -b + or - the square root of the quantity b(squared) -4ac all over 2a

    idk what the 3rd is;; substitution or synthetic division?

  • 1 decade ago

    The last one is complete the square

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  • 1 decade ago

    do your own homework.

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