(x-4)(x+2)=0 By Quadratic Formula

2 min read Jun 17, 2024

Solving (x-4)(x+2) = 0 using the Quadratic Formula

This equation can be solved in a couple of ways, but we'll focus on using the quadratic formula for this example.

Understanding the Quadratic Formula

The quadratic formula is a powerful tool for solving equations in the form of ax² + bx + c = 0. It provides the solutions for x as:

x = (-b ± √(b² - 4ac)) / 2a

Where:

a, b, and c are the coefficients of the quadratic equation.

Expanding the Equation

Before we can apply the quadratic formula, we need to expand the given equation:

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

This expands to:

x² - 2x - 8 = 0

Now, we can identify the coefficients:

a = 1
b = -2
c = -8

Applying the Quadratic Formula

Let's substitute the values into the quadratic formula:

x = (2 ± √((-2)² - 4 * 1 * -8)) / (2 * 1)

Simplifying the equation:

x = (2 ± √(4 + 32)) / 2

x = (2 ± √36) / 2

x = (2 ± 6) / 2

Finding the Solutions

Now, we have two possible solutions:

x = (2 + 6) / 2 = 8 / 2 = 4
x = (2 - 6) / 2 = -4 / 2 = -2

Therefore, the solutions to the equation (x - 4)(x + 2) = 0 are x = 4 and x = -2.

Conclusion

The quadratic formula provides a systematic approach to solving quadratic equations, even when they are initially presented in factored form. This method ensures we can find all possible solutions and avoid overlooking any potential values of x.