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Solving the Equation: (x + 2)(x - 5) = 0
This equation is a simple quadratic equation, but it's presented in a way that makes it easy to solve 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.
Let's break down the steps to solve this equation:
1. Identify the factors
The equation is already factored for us: (x + 2)(x - 5) = 0
We have two factors: (x + 2) and (x - 5)
2. Apply the Zero Product Property
For the product of these factors to be zero, one or both of them must equal zero.
Therefore, we have two possible scenarios:
- Scenario 1: (x + 2) = 0
- Scenario 2: (x - 5) = 0
3. Solve for x in each scenario
-
Scenario 1: (x + 2) = 0
- Subtract 2 from both sides: x = -2
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Scenario 2: (x - 5) = 0
- Add 5 to both sides: x = 5
Conclusion
The solutions to the equation (x + 2)(x - 5) = 0 are x = -2 and x = 5.
These are the values of x that make the equation true. You can verify this by plugging each value back into the original equation.