(x-4)%3D960.jpeg "(x+12)(x-4)=960")
Solving the Equation: (x+12)(x-4)=960
This article will guide you through the process of solving the quadratic equation (x+12)(x-4)=960.
1. Expanding the Equation
First, we need to expand the left side of the equation by using the distributive property (or FOIL method):
(x+12)(x-4) = x² - 4x + 12x - 48
Simplifying the expression:
x² + 8x - 48 = 960
2. Rearranging the Equation
To solve the quadratic equation, we need to set it equal to zero:
x² + 8x - 1008 = 0
3. Factoring the Equation
Now, we need to factor the quadratic expression. We need to find two numbers that multiply to -1008 and add up to 8. These numbers are 36 and -28:
(x + 36)(x - 28) = 0
4. Solving for x
Finally, we can solve for x by setting each factor equal to zero:
- x + 36 = 0 => x = -36
- x - 28 = 0 => x = 28
5. Conclusion
Therefore, the solutions to the equation (x+12)(x-4)=960 are x = -36 and x = 28.