What are the solutions to the equation? 7x^3=28x

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What are the solutions to the equation?
7x^3=28x

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    2022-01-06T01:22:27+00:00

    7x³ = 28x is our equation. We want its solutions.

    When you have x and different powers, set the whole thing equal to zero.

    7x³ = 28x

    7x³ – 28x = 0

    Now notice there’s a common x in both terms. Let’s factor it out.

    x (7x² – 28) = 0

    As 7 is a factor of 7 and 28, it too can be factored out.

    x (7) (x² – 4) = 0

    We can further factor x² – 4. We want a pair of numbers that multiply to 4 and whose sum is zero. The pairs are 1 and 4, 2 and 2. If we add 2 and -2 we get zero.

    x (7) (x – 2) (x + 2) = 0

    Now we use the Zero Product Property – if some product multiplies to zero, so do its pieces.

    x = 0        —–> so x = 0

    7 = 0       —–> no solution

    x – 2 = 0   —-> so x = 2   after adding 2 to both sides

    x + 2 = 0  —> so = x – 2  after subtracting 2 to both sides

    Thus the solutions are x = 0, x = 2, x = -2.

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