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

2 min read Jun 17, 2024

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

This equation represents a simple quadratic equation in factored form. Let's break down how to solve it:

Understanding 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 equal to zero, then at least one of the factors must be equal to zero.

Applying the Property

In our equation, (x-1) and (x-7) are the factors. Therefore, for the product to be zero, at least one of these factors must be zero. This gives us two possibilities:

x - 1 = 0
x - 7 = 0

Solving for x

Now, we simply solve each of these equations for x:

x - 1 = 0 => x = 1
x - 7 = 0 => x = 7

Solutions

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

Verification

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

For x = 1: (1-1)(1-7) = 0 * 0 = 0
For x = 7: (7-1)(7-7) = 6 * 0 = 0

Since both solutions satisfy the original equation, we have confirmed that our answers are correct.