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

Jasonbradley

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Jun 17, 2024

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

This equation is a quadratic equation in factored form. The key to solving this equation lies in understanding 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.

Using the Zero Product Property

1. Set each factor equal to zero:

   • x - 5 = 0
   • x + 3 = 0

2. Solve each equation for x:

   • x = 5
   • x = -3

Solutions

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

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = 5: (5 - 5)(5 + 3) = 0 * 8 = 0. This confirms that x = 5 is a solution.
• For x = -3: (-3 - 5)(-3 + 3) = -8 * 0 = 0. This confirms that x = -3 is a solution.

Conclusion

In conclusion, the solutions to the equation (x-5)(x+3)=0 are x = 5 and x = -3. This demonstrates how the Zero Product Property provides a straightforward approach for solving quadratic equations in factored form.