(x+7)(x-1)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x + 7)(x - 1) = 0

This equation is a quadratic equation in factored form. Let's understand how to solve it:

The Zero Product Property

The key to solving this equation lies in the Zero Product Property. This 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 case, we have two factors: (x + 7) and (x - 1). To make the product equal to zero, one or both of these factors must be equal to zero.

Solving for x

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

• Factor 1: x + 7 = 0

  • Subtracting 7 from both sides, we get: x = -7

• Factor 2: x - 1 = 0

  • Adding 1 to both sides, we get: x = 1

Solutions

Therefore, the solutions to the equation (x + 7)(x - 1) = 0 are x = -7 and x = 1.

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = -7: (-7 + 7)(-7 - 1) = 0 * -8 = 0. This is true.
• For x = 1: (1 + 7)(1 - 1) = 8 * 0 = 0. This is also true.

This confirms that our solutions are correct.