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

2 min read Jun 17, 2024

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

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy this equation, we can use the Zero Product Property.

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 to Our Equation

In our equation, we have two factors: (x-8) and (x+8). Therefore, for the product to be zero, at least one of these factors must be zero.

We can set each factor equal to zero and solve for x:

x-8 = 0 Adding 8 to both sides, we get: x = 8
x+8 = 0 Subtracting 8 from both sides, we get: x = -8

Solutions

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

Verifying the Solutions

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

For x = 8: (8-8)(8+8) = 0 * 16 = 0. This is true.
For x = -8: (-8-8)(-8+8) = -16 * 0 = 0. This is also true.

Conclusion

We have successfully solved the equation (x-8)(x+8)=0 using the Zero Product Property. The solutions are x = 8 and x = -8. This demonstrates how factoring can be a powerful tool in solving quadratic equations.