(x%2B8)%3D0.jpeg "(x-3)(x+8)=0")
Solving the Equation (x-3)(x+8) = 0
This equation is a simple example of 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 equal to zero, then at least one of the factors must be equal to zero.
In our equation, (x-3)(x+8) = 0, we have two factors: (x-3) and (x+8). Therefore, for the product to be zero, either:
- (x-3) = 0 or
- (x+8) = 0
Solving for x
Let's solve each equation separately:
-
(x-3) = 0
- Add 3 to both sides: x = 3
-
(x+8) = 0
- Subtract 8 from both sides: x = -8
The Solutions
Therefore, the solutions to the equation (x-3)(x+8) = 0 are x = 3 and x = -8. These are the values of x that make the equation true.
Verification
We can verify our solutions by substituting them back into the original equation:
- For x = 3: (3-3)(3+8) = 0 * 11 = 0 (True)
- For x = -8: (-8-3)(-8+8) = -11 * 0 = 0 (True)
Since both solutions make the equation true, we have successfully solved the equation (x-3)(x+8) = 0.