algebra

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in solving the equation (x +2)(x - 2) = 32 eric stated the solution to be x + 2 = 32 => x = 30 or x- 2 = 32 => x = 34. however at least one of these solutions fails to work when plugged back into the equation. why is that? please help eric to understand the problem better; solve the problem yourself and explain your reasoning.

i tried using foil that doesnt appear to work

  • algebra -

    knowing the product of two numbers does not tell you anything about what the numbers are, unless the product is zero.

    If the product is zero, then at least one of the numbers must be zero.

    (x +2)(x - 2) = 32
    x^2 - 4 = 32
    x^2 - 36 = 0
    (x-6)(x+6) = 0

    Now you have two numbers whose product is zero. So, x must be 6 or -6.

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