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9 May, 17:14

Solve each quadratic equation by factoring and using the zero product property.

x^2 - 8x + 30 = 3x

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Answers (2)
  1. 9 May, 17:25
    0
    x = 5 or x = 6

    Step-by-step explanation:

    Given equation is:

    x²-8x+30 = 3x

    adding - 3x to both sides of above equation, we get

    x²-8x+30-3x = 3x-3x

    add like terms

    x²-11x+30 = 0

    we solve this equation by factoring.

    split the middle term so that the product of two numbers should be 30 and the sum is - 11.

    x²-6x-5x+30 = 0

    make two groups

    x (x-6) - 5 (x-6) = 0

    take (x-6) as common

    (x-6) (x-5) = 0

    Applying Zero-Product Property to above equation, we get

    x-6 = 0 or x-5 = 0

    first solve x-6 = 0

    adding 6 to both sides of above equation, we get

    x-6+6 = 0+6

    x+0 = 6

    x = 6

    secondly, solve this x-5 = 0

    adding 5 to above equation, we get

    x-5+5 = 0+5

    x + 0 = 5

    x = 5

    Hence, the solution of x²-8x+30 = 3x is {6,5}.
  2. 9 May, 17:31
    0
    x=5 x=6

    Step-by-step explanation:

    x^2 - 8x + 30 = 3x

    Subtract 3x from each side

    x^2 - 8x-3x + 30 = 3x-3x

    x^2 - 11x + 30 = 0

    What 2 numbers multiply to 30 and add to - 11

    -5*-6 = 30

    -5+-6 = - 11

    (x-5) (x-6) = 0

    Using the zero product property

    x-5 = 0 and x-6 = 0

    x-5+5 = 0+5 and x-6+6 = 0+6

    x=5 x=6
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