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Solving the Equation (x-5)(x+6) = 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 zero, then at least one of the factors must be zero.
Applying the Zero Product Property
In our equation, we have two factors: (x-5) and (x+6). To make the product equal to zero, we need to set each factor equal to zero and solve for x.
1. Set the first factor to zero:
x - 5 = 0
Add 5 to both sides:
x = 5
2. Set the second factor to zero:
x + 6 = 0
Subtract 6 from both sides:
x = -6
Solutions
Therefore, the solutions to the equation (x-5)(x+6) = 0 are x = 5 and x = -6.
These solutions represent the points where the graph of the quadratic equation intersects the x-axis.
Conclusion
By applying the Zero Product Property, we efficiently solved the quadratic equation in factored form and found the two values of x that satisfy the equation. This method is a powerful tool for solving equations involving products of factors.