(x%2B7)%3D0.jpeg "(x-5)(x+7)=0")
Solving the Equation (x - 5)(x + 7) = 0
This equation represents a simple quadratic equation in factored form. To find the solutions for x, 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 equal to zero, then at least one of the factors must be zero.
In our equation, (x - 5) and (x + 7) are the two factors. Therefore, for the product to equal zero, either:
- (x - 5) = 0 or
- (x + 7) = 0
Solving for x
Now we can solve for x in each of these equations:
-
x - 5 = 0
- Adding 5 to both sides, we get: x = 5
-
x + 7 = 0
- Subtracting 7 from both sides, we get: x = -7
Solutions
Therefore, the solutions to the equation (x - 5)(x + 7) = 0 are x = 5 and x = -7.
Conclusion
By applying the Zero Product Property, we easily solved the equation and found the two values of x that make the equation true. This method simplifies solving quadratic equations in factored form.