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Solving the Equation (x-9)(x-7) = 0
This equation represents 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 equal to zero, then at least one of the factors must be equal to zero.
Let's break down the steps to solve this equation:
1. Identify the Factors
The equation is already factored: (x-9)(x-7) = 0
We have two factors: (x-9) and (x-7).
2. Apply the Zero Product Property
According to the Zero Product Property, for the product to be zero, at least one of the factors must be zero. Therefore, we have two possibilities:
- (x-9) = 0
- (x-7) = 0
3. Solve for x
Now, we need to solve each equation for 'x':
- x - 9 = 0 => x = 9
- x - 7 = 0 => x = 7
Conclusion
Therefore, the solutions to the equation (x-9)(x-7) = 0 are x = 9 and x = 7.