(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 simple quadratic equation that can be solved using 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.

Applying the Zero Product Property

1. Identify the factors: In the equation (x-7)(x-1) = 0, the factors are (x-7) and (x-1).

2. Set each factor equal to zero:

   • (x-7) = 0
   • (x-1) = 0

3. Solve for x in each equation:

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

Solutions

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

Checking the Solutions

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

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

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

Since both solutions satisfy the original equation, we have confirmed that they are indeed the correct solutions.