(x%2B7)%3D0.jpeg "(x-1)(x+7)=0")
Solving the Equation: (x - 1)(x + 7) = 0
This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the 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 Zero Product Property
In our equation, (x - 1)(x + 7) = 0, we have two factors: (x - 1) and (x + 7). According to the Zero Product Property, for this equation to be true, either:
- x - 1 = 0
- x + 7 = 0
Solving for x
Now we can solve each of these simple linear equations:
- x - 1 = 0 => x = 1
- x + 7 = 0 => x = -7
Conclusion
Therefore, the solutions to the equation (x - 1)(x + 7) = 0 are x = 1 and x = -7. These are the values of x that make the equation true.