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Solving the Equation (x-5)(x+4)=0
This equation is a simple quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can use 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.
Let's apply this to our equation:
(x-5)(x+4) = 0
This equation implies that either (x-5) = 0 or (x+4) = 0.
Solving for x in each case:
- x - 5 = 0
- Add 5 to both sides: x = 5
- x + 4 = 0
- Subtract 4 from both sides: x = -4
Therefore, the solutions to the equation (x-5)(x+4) = 0 are x = 5 and x = -4.
Understanding the Solution
These solutions represent the points where the graph of the quadratic function y = (x-5)(x+4) intersects the x-axis. The x-intercepts of a graph occur when y = 0, which corresponds to the solutions of the equation.
In this case, the graph of y = (x-5)(x+4) is a parabola that intersects the x-axis at the points x = 5 and x = -4.
Conclusion
Solving the equation (x-5)(x+4) = 0 using the Zero Product Property provides us with two solutions: x = 5 and x = -4. These solutions are crucial for understanding the behavior of the corresponding quadratic function and its graph.