(x%2B7)-0.jpeg "(x-4)(x+7) 0")
Solving the Equation (x-4)(x+7) = 0
This equation represents a quadratic expression set equal to zero. To solve for x, we can utilize the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
Let's break down the equation:
- (x - 4): This is the first factor.
- (x + 7): This is the second factor.
To satisfy the Zero Product Property, either:
-
(x - 4) = 0
- Solving for x, we get x = 4
-
(x + 7) = 0
- Solving for x, we get x = -7
Therefore, the solutions to the equation (x-4)(x+7) = 0 are x = 4 and x = -7.
In conclusion, by applying the Zero Product Property, we efficiently found the two values of x that make the equation true. These solutions represent the points where the graph of the quadratic function intersects the x-axis.