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(x+5)(x-5)(x+5)(x-1)=0

2 min read Jun 17, 2024
(x+5)(x-5)(x+5)(x-1)=0

Solving the Equation (x+5)(x-5)(x+5)(x-1) = 0

This equation is a polynomial equation in factored form, which makes solving it relatively straightforward. Here's how we can find the solutions:

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, we have four factors:

  • (x + 5)
  • (x - 5)
  • (x + 5)
  • (x - 1)

For the entire product to be zero, at least one of these factors must equal zero.

Finding the Solutions

Let's set each factor equal to zero and solve for x:

  1. (x + 5) = 0 Subtracting 5 from both sides gives us x = -5

  2. (x - 5) = 0 Adding 5 to both sides gives us x = 5

  3. (x + 5) = 0 This is the same factor as the first, so we already have the solution x = -5

  4. (x - 1) = 0 Adding 1 to both sides gives us x = 1

The Solutions

Therefore, the solutions to the equation (x+5)(x-5)(x+5)(x-1) = 0 are:

  • x = -5 (this solution appears twice, but we only list it once)
  • x = 5
  • x = 1

This means that if we substitute any of these values of x back into the original equation, the equation will be true.

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