(x-2)(x+4)=7

3 min read Jun 17, 2024

Solving the Quadratic Equation (x-2)(x+4)=7

This equation involves a quadratic expression and we need to solve for the values of x that satisfy the equation. Here's how we can approach this:

First, we need to expand the left-hand side of the equation by multiplying the factors:

(x-2)(x+4) = x² + 2x - 8

Now, our equation becomes:

x² + 2x - 8 = 7

To solve a quadratic equation, we need it in standard form (ax² + bx + c = 0). Let's move the constant term to the left side:

x² + 2x - 15 = 0

Now we have a standard quadratic equation. We can solve this using various methods:

Factoring: If possible, we can factor the quadratic expression into two binomials. In this case, we can factor it as: (x + 5)(x - 3) = 0 Therefore, the solutions are: x + 5 = 0 => x = -5 x - 3 = 0 => x = 3
Quadratic Formula: If factoring isn't immediately obvious, we can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 2, and c = -15 (from our standard form equation).

Plugging in the values:

x = (-2 ± √(2² - 4 * 1 * -15)) / 2 * 1 x = (-2 ± √(64)) / 2 x = (-2 ± 8) / 2

This gives us two solutions:

x = (-2 + 8) / 2 = 3 x = (-2 - 8) / 2 = -5

Therefore, the solutions to the equation (x-2)(x+4)=7 are x = 3 and x = -5.