(x-3)(x+5)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-3)(x+5)=0

This equation represents a simple quadratic equation in factored form. We can solve it using the Zero Product Property, which states that if the product of two 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 - 3 = 0
   • x + 5 = 0

2. Solve for x in each equation:

   • x = 3
   • x = -5

Solution: Therefore, the solutions to the equation (x-3)(x+5)=0 are x = 3 and x = -5.

Explanation:

The equation represents a parabola that intersects the x-axis at two points, x = 3 and x = -5. These are the roots of the equation, which are the values of x where the equation equals zero.

Verification:

We can verify our solution by substituting the values of x back into the original equation:

• For x = 3: (3 - 3)(3 + 5) = (0)(8) = 0
• For x = -5: (-5 - 3)(-5 + 5) = (-8)(0) = 0

As we can see, both solutions satisfy the original equation.

Conclusion: By applying the Zero Product Property, we were able to efficiently solve the quadratic equation (x-3)(x+5)=0 and obtain the solutions x = 3 and x = -5. These solutions represent the points where the parabola intersects the x-axis.