(x-2)(x-7)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-2)(x-7)=0

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

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 case, we have two factors: (x-2) and (x-7).

Solving for x

1. Set each factor equal to zero:

   • x - 2 = 0
   • x - 7 = 0

2. Solve for x in each equation:

   • x = 2
   • x = 7

The Solution

Therefore, the solutions to the equation (x-2)(x-7) = 0 are x = 2 and x = 7.

Verification

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

• For x = 2: (2-2)(2-7) = 0 * -5 = 0. This is true.
• For x = 7: (7-2)(7-7) = 5 * 0 = 0. This is also true.

This confirms that both x = 2 and x = 7 are valid solutions to the equation.