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Solving the Equation (x-9)(x+2)=0
The equation (x-9)(x+2)=0 is a quadratic equation in factored form. This means that the equation is already set up to be easily solved.
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. This is the key to solving our equation.
Solving for x
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Set each factor equal to zero:
- x - 9 = 0
- x + 2 = 0
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Solve each equation for x:
- x = 9
- x = -2
The Solutions
Therefore, the solutions to the equation (x-9)(x+2)=0 are x = 9 and x = -2.
Checking our Solutions
We can check our solutions by plugging them back into the original equation:
- For x = 9: (9 - 9)(9 + 2) = (0)(11) = 0
- For x = -2: (-2 - 9)(-2 + 2) = (-11)(0) = 0
Both solutions satisfy the equation, confirming that our answers are correct.
Conclusion
By utilizing the Zero Product Property, we were able to easily solve the equation (x-9)(x+2)=0 and find the two solutions: x = 9 and x = -2. This method is a powerful tool for solving quadratic equations that are already factored.