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

Question

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## Answers ( No )

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.