(x-9)(x-8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-9)(x-8) = 0

This equation represents a simple quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can use the Zero Product Property.

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.

Solving the Equation

1. Identify the factors: The equation (x-9)(x-8) = 0 shows two factors: (x-9) and (x-8).

2. Apply the Zero Product Property: For the product of the two factors to equal zero, one or both of the factors must be equal to zero.

3. Set each factor to zero and solve:

   • x - 9 = 0 => x = 9
   • x - 8 = 0 => x = 8

Solution

Therefore, the solutions to the equation (x-9)(x-8) = 0 are x = 9 and x = 8.

Verification

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

• For x = 9: (9-9)(9-8) = 0 * 1 = 0
• For x = 8: (8-9)(8-8) = -1 * 0 = 0

Both solutions satisfy the original equation.