(x+3)(x+7)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+3)(x+7) = 0

The equation (x+3)(x+7) = 0 is a quadratic equation in factored form. This form makes it particularly easy to solve for the values of x that satisfy the equation.

Understanding the Zero Product Property

The key to solving this equation lies in 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 zero.

Applying the Zero Product Property

1. Identify the factors: In our equation, the factors are (x+3) and (x+7).

2. Set each factor equal to zero:

   • x + 3 = 0
   • x + 7 = 0

3. Solve for x in each equation:

   • x = -3
   • x = -7

The Solutions

Therefore, the solutions to the equation (x+3)(x+7) = 0 are x = -3 and x = -7.

Verification

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

• For x = -3: (-3 + 3)(-3 + 7) = 0 * 4 = 0
• For x = -7: (-7 + 3)(-7 + 7) = -4 * 0 = 0

Both solutions satisfy the equation, confirming our results.

Conclusion

By utilizing the Zero Product Property, we effectively solved the factored quadratic equation (x+3)(x+7) = 0, finding the solutions x = -3 and x = -7. This approach simplifies the process of finding the roots of a quadratic equation when it is presented in factored form.