(x-12)(x+4)=9

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x-12)(x+4) = 9

This article will guide you through the process of solving the quadratic equation (x-12)(x+4) = 9. We'll break down the steps and explain the concepts involved.

Step 1: Expand the Left Side

First, we need to expand the left side of the equation by multiplying the two binomials:

(x-12)(x+4) = x² - 8x - 48

Step 2: Move Constant Term to the Left Side

Next, we move the constant term (9) from the right side to the left side, making the equation:

x² - 8x - 48 - 9 = 0

Step 3: Simplify the Equation

Now, we simplify the equation:

x² - 8x - 57 = 0

Step 4: Factor the Quadratic Expression

The quadratic expression on the left side can be factored as:

(x - 19)(x + 3) = 0

Step 5: Solve for x

For the product of two factors to be zero, at least one of them must be zero. Therefore, we have two possible solutions:

x - 19 = 0 or x + 3 = 0

Solving for x in each case:

x = 19 or x = -3

Conclusion

Therefore, the solutions to the quadratic equation (x-12)(x+4) = 9 are x = 19 and x = -3.