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Solving the Equation (x-7)(x+7) = 0
This equation is a simple example of a 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 equation, (x-7) and (x+7) are the two factors. Therefore, for the product to be zero, one or both of these factors must equal zero.
Solving for x
We can now set each factor equal to zero and solve for x:
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Factor 1: x - 7 = 0
- Adding 7 to both sides: x = 7
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Factor 2: x + 7 = 0
- Subtracting 7 from both sides: x = -7
Solutions
Therefore, the solutions to the equation (x-7)(x+7) = 0 are x = 7 and x = -7.
Verifying the Solutions
We can check our solutions by plugging them back into the original equation:
- For x = 7: (7-7)(7+7) = 0 * 14 = 0
- For x = -7: (-7-7)(-7+7) = -14 * 0 = 0
Both solutions satisfy the original equation, confirming their validity.
Conclusion
Solving the equation (x-7)(x+7) = 0 using the Zero Product Property is a straightforward process. By setting each factor equal to zero, we can find the two distinct solutions, x = 7 and x = -7.