(x+2)(x+8)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+2)(x+8)=0

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

1. Set each factor equal to zero:

   • x + 2 = 0
   • x + 8 = 0

2. Solve for x in each equation:

   • x = -2
   • x = -8

Solutions

Therefore, the solutions to the equation (x+2)(x+8)=0 are x = -2 and x = -8.

Graphical Interpretation

The equation represents a parabola that intersects the x-axis at the points (-2, 0) and (-8, 0). These points correspond to the solutions we found using the Zero Product Property.

Conclusion

By applying the Zero Product Property, we have successfully found the solutions to the quadratic equation (x+2)(x+8)=0. The solutions are x = -2 and x = -8, which represent the x-intercepts of the parabola defined by the equation.