(x%2B3)%3D24.jpeg "(x-7)(x+3)=24")
Solving the Equation: (x-7)(x+3) = 24
This equation involves a product of two binomials equaling a constant. To solve it, we need to follow these steps:
1. Expand the Left Side
First, we need to expand the left side of the equation using the distributive property (or FOIL method):
(x-7)(x+3) = x² + 3x - 7x - 21 = x² - 4x - 21
Now our equation becomes: x² - 4x - 21 = 24
2. Move the Constant to the Left Side
To solve this quadratic equation, we need to set it equal to zero. We can do this by subtracting 24 from both sides:
x² - 4x - 45 = 0
3. Factor the Quadratic Expression
Now we need to factor the quadratic expression on the left side:
(x - 9)(x + 5) = 0
4. Solve for x
For the product of two factors to equal zero, at least one of the factors must be zero. Therefore:
- x - 9 = 0 => x = 9
- x + 5 = 0 => x = -5
Solution
The solutions to the equation (x-7)(x+3) = 24 are x = 9 and x = -5.