(x-2)(x+4)+9=0

2 min read Jun 17, 2024
(x-2)(x+4)+9=0

Solving the Quadratic Equation: (x-2)(x+4) + 9 = 0

This article will guide you through the process of solving the quadratic equation (x-2)(x+4) + 9 = 0.

Expanding and Simplifying the Equation

First, we need to expand the equation by multiplying the terms in the parentheses:

(x-2)(x+4) + 9 = 0

x² + 4x - 2x - 8 + 9 = 0

Combining like terms, we get:

x² + 2x + 1 = 0

Solving by Factoring

This equation can be factored into:

(x+1)(x+1) = 0

Therefore, the solution is:

x = -1

Solving by the Quadratic Formula

The quadratic formula is a general solution for equations in the form ax² + bx + c = 0. In this case, a = 1, b = 2, and c = 1.

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values:

x = (-2 ± √(2² - 4 * 1 * 1)) / (2 * 1)

x = (-2 ± √0) / 2

x = -1

Conclusion

Both methods, factoring and using the quadratic formula, arrive at the same solution: x = -1.

It's important to remember that quadratic equations can have up to two solutions. In this particular case, we have a double root, meaning the solution x = -1 appears twice.

Featured Posts