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9 February, 11:58

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

10x + 6 = - 2x^2 - 2

+1
Answers (2)
  1. 9 February, 12:34
    0
    x = - 4 or x = - 1

    Step-by-step explanation:

    Given equation is:

    10x+6 = - 2x²-2

    Adding 2x² and 2 to both sides of above equation, we get

    2x²+2 + 10x+6 = - 2x²-2 + 2x²+2

    Adding like terms, we get

    2x²+10x+8 = 0

    As we have noticed that there are multiples of 2.

    Taking 2 as common, we get

    2 (x²+5x+4) = 0

    Multiplying by 1/2 to both sides of above equation, we get

    1/2.2 (x²+5x+4) = 1/2.0

    x²+5x+4 = 0

    Split the middle term of above equation so that the sum of two term should be 5 and their product be 4.

    x²+4x+x+4 = 0

    Making two groups, we get

    x (x+4) + 1 (x+4)

    Taking (x+4) common, we get

    (x+4) (x+1) = 0

    Applying Zero-Product Property to above equation, we get

    x+4 = 0 or x+1 = 0

    Firstly, solve x+4 = 0

    Adding - 4 to both sides of above equation, we get

    x+4-4 = 0-4

    x + 0 = - 4

    x = - 4

    Secondly, solve x+1 = 0

    Adding - 1 to both sides of above equation, we get

    x+1-1 = 0-1

    x = - 1

    Hence, the solution of 10x+6 = - 2x²-2 is {-4,-1}.
  2. 9 February, 14:50
    0
    x = - 4 x=-1

    Step-by-step explanation:

    10x + 6 = - 2x^2 - 2

    Add 2x^2 to each side

    +2x^2 + 10x + 6 = 2x^2 - 2x^2 - 2

    2x^2 + 10x + 6 = - 2

    Add 2 to each side

    2x^2 + 10x + 6+2 = - 2+2

    2x^2 + 10x + 8 = 0

    Divide each side by 2

    2/2x^2 + 10/2x + 8/2 = 0/2

    x^2 + 5x+4 = 0

    What 2 numbers multiply to 4 and add to 5

    4*1 = 4

    4+1 = 5

    (x+4) (x+1) = 0

    Using the zero product property

    x+4 = 0 x+1 = 0

    x+4-4 = 0-4 x+1-1 = 0-1

    x = - 4 x=-1
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