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Solving the Equation (x - 9)(x + 3) = 0
This equation represents a quadratic equation in factored form. To solve for the values of 'x' that satisfy the equation, we can utilize the Zero Product Property.
Zero Product Property
The Zero Product 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.
Solving the Equation
Applying the Zero Product Property to our equation, we get:
- x - 9 = 0 or x + 3 = 0
Solving for 'x' in each equation:
- x = 9 or x = -3
Therefore, the solutions to the equation (x - 9)(x + 3) = 0 are x = 9 and x = -3.
Graphical Interpretation
Graphically, these solutions represent the x-intercepts of the parabola represented by the equation (x - 9)(x + 3) = 0. These intercepts are the points where the parabola crosses the x-axis.
Conclusion
The Zero Product Property provides a straightforward method for solving quadratic equations in factored form. By setting each factor equal to zero and solving, we can determine the values of 'x' that satisfy the equation. These solutions have a significant graphical interpretation as the x-intercepts of the parabola represented by the equation.