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Solving the Equation (x+7)(x-5)=0
The equation (x+7)(x-5)=0 is 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.
Applying the Zero Product Property
Let's apply this property to our equation:
- Identify the factors: We have two factors: (x+7) and (x-5).
- Set each factor equal to zero:
- x + 7 = 0
- x - 5 = 0
- Solve for x:
- x = -7
- x = 5
Therefore, the solutions to the equation (x+7)(x-5)=0 are x = -7 and x = 5.
Verifying the Solutions
We can verify our solutions by plugging them back into the original equation:
- For x = -7:
- (-7 + 7)(-7 - 5) = (0)(-12) = 0
- For x = 5:
- (5 + 7)(5 - 5) = (12)(0) = 0
Since both solutions result in 0 when substituted into the equation, they are indeed the correct solutions.
Conclusion
The equation (x+7)(x-5)=0 can be easily solved using the Zero Product Property. This method involves identifying the factors, setting them equal to zero, and solving for x. The solutions to the equation are x = -7 and x = 5, which can be verified by substituting them back into the original equation.