(x+6)(x-5)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+6)(x-5) = 0

This equation represents a quadratic expression in factored form. To find the solutions for x, we can utilize 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.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • x + 6 = 0
   • x - 5 = 0

2. Solve for x in each equation:

   • x = -6
   • x = 5

Solutions

Therefore, the solutions to the equation (x+6)(x-5) = 0 are x = -6 and x = 5.

Graphical Interpretation

The solutions we found represent the x-intercepts of the parabola defined by the equation y = (x+6)(x-5). This means the graph of the parabola will intersect the x-axis at the points (-6, 0) and (5, 0).

Conclusion

By applying the Zero Product Property, we successfully solved the equation (x+6)(x-5) = 0 and determined the solutions to be x = -6 and x = 5. These solutions hold significance in the graphical representation of the equation, indicating the points where the parabola intersects the x-axis.