(x+8)(x-8)=0

Jasonbradley

2 min read

·

Jun 17, 2024

12

Share

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

This equation is a quadratic equation in factored form. Here's how to solve it:

Understanding the Zero Product Property

The Zero Product 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 Property

In the equation (x+8)(x-8) = 0, we have two factors: (x+8) and (x-8). To make the product zero, one or both of these factors must equal zero.

Solving for x

1. Set each factor equal to zero:

   • x + 8 = 0
   • x - 8 = 0

2. Solve for x in each equation:

   • x = -8
   • x = 8

Solutions

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

Verification

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

• For x = -8: (-8 + 8)(-8 - 8) = (0)(-16) = 0
• For x = 8: (8 + 8)(8 - 8) = (16)(0) = 0

Both solutions satisfy the equation.

Conclusion

By applying the Zero Product Property, we successfully solved the quadratic equation (x+8)(x-8) = 0 and found two distinct solutions: x = -8 and x = 8.