(x+2)(x-4)=72

3 min read Jun 16, 2024

Solving the Quadratic Equation: (x+2)(x-4) = 72

This article will guide you through the steps of solving the quadratic equation (x+2)(x-4) = 72. We'll break down the process and demonstrate how to find the solutions for x.

Expanding the Equation

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

(x+2)(x-4) = x² - 2x - 8

Now our equation becomes:

x² - 2x - 8 = 72

Rearranging into Standard Form

To solve for x, we need to rearrange the equation into standard quadratic form, which is:

ax² + bx + c = 0

Subtracting 72 from both sides of our equation gives us:

x² - 2x - 80 = 0

Solving the Quadratic Equation

Now we have a quadratic equation in standard form. There are a few ways to solve this:

1. Factoring:

Find two numbers that multiply to -80 and add up to -2. These numbers are -12 and 6.
Rewrite the equation as: (x-12)(x+6) = 0
Set each factor equal to zero and solve for x:
- x - 12 = 0 => x = 12
- x + 6 = 0 => x = -6

2. Quadratic Formula:

The quadratic formula is a general solution for any quadratic equation in standard form:

x = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 1, b = -2, and c = -80.
Substitute these values into the quadratic formula and simplify to find the solutions for x.

3. Completing the Square:

This method involves manipulating the equation to create a perfect square trinomial. We can then take the square root of both sides to solve for x.

Solutions

No matter which method you choose, you'll find the two solutions for the equation (x+2)(x-4) = 72 are:

x = 12 and x = -6