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Solving the Equation (x-9)(x+7) = 0
This equation is a simple quadratic equation presented in factored form. Let's break down how to solve it and understand the concept behind it.
The Zero Product Property
The key to solving this equation lies in 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.
In our case, the factors are (x-9) and (x+7). Therefore, for the product to be zero, either:
- (x-9) = 0
- (x+7) = 0
Solving for x
Let's solve each equation separately:
-
For (x-9) = 0:
- Add 9 to both sides: x = 9
-
For (x+7) = 0:
- Subtract 7 from both sides: x = -7
The Solutions
Therefore, the solutions to the equation (x-9)(x+7) = 0 are x = 9 and x = -7.
Visual Representation
You can visualize these solutions on a number line. The solutions represent the x-intercepts of the parabola represented by the equation (x-9)(x+7) = 0.
Conclusion
By applying the Zero Product Property, we effectively solved a quadratic equation in factored form. This method provides a straightforward and efficient way to find the solutions to such equations.