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10 September, 06:48

Use the zero product property to find the solutions to the equation 6x^2 - 5x = 56.

x = - 8 or x = 7/6

x = -8/3 or x = 7/2

x = -1/2 or x = 56/3

x = - 3/7 or x = 2/3

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Answers (2)
  1. 10 September, 09:25
    0
    Step-by-step explanation:

    solving for x

    6x²-5x=56

    subtract 56 from both sides

    6x²-5x-56=0

    using middle term break method

    factorise (56) (6) = (2*2*2*7) (2*3)

    = (2*2*2*2) makes 16 and combining (3*7) makes 21

    so we have

    =6x²+16x-21x-56=0

    taking factors out of first two terms and then other two terms

    =>2x (3x+8) - 7 (3x+8) = 0

    => (2x-7) (3x+8) = 0

    either 2x-7=0 or 3x+8=0

    2x=7 or 3x=-8

    x=7/2 or x=-8/3
  2. 10 September, 10:22
    0
    x = 7/2 or x = - 8/3

    Step-by-step explanation:

    Solve for x over the real numbers:

    6 x^2 - 5 x = 56

    Divide both sides by 6:

    x^2 - (5 x) / 6 = 28/3

    Add 25/144 to both sides:

    x^2 - (5 x) / 6 + 25/144 = 1369/144

    Write the left hand side as a square:

    (x - 5/12) ^2 = 1369/144

    Take the square root of both sides:

    x - 5/12 = 37/12 or x - 5/12 = - 37/12

    Add 5/12 to both sides:

    x = 7/2 or x - 5/12 = - 37/12

    Add 5/12 to both sides:

    Answer: x = 7/2 or x = - 8/3
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