(x+5)(x+6)=2(3x+4)

3 min read Jun 16, 2024

Solving the Equation (x+5)(x+6) = 2(3x+4)

This article will guide you through the steps of solving the equation (x+5)(x+6) = 2(3x+4).

First, we need to expand both sides of the equation to get rid of the parentheses.

Now our equation looks like this: x² + 11x + 30 = 6x + 8

To solve for x, we need to have all the terms on one side of the equation. We can achieve this by subtracting 6x and 8 from both sides:

x² + 11x + 30 - 6x - 8 = 0

This simplifies to: x² + 5x + 22 = 0

We now have a quadratic equation in the form ax² + bx + c = 0. There are a couple of ways to solve this:

Factoring: In this case, the equation doesn't factor easily.
Quadratic Formula: The quadratic formula is a general solution to all quadratic equations. It states that:

x = [-b ± √(b² - 4ac)] / 2a

Where:
- a = 1
- b = 5
- c = 22
Plugging these values into the formula:

x = [-5 ± √(5² - 4 * 1 * 22)] / 2 * 1 x = [-5 ± √(-63)] / 2 x = [-5 ± √63 * i] / 2 (where 'i' is the imaginary unit, √-1)

Therefore, the solutions to the equation are:

x = (-5 + √63 * i) / 2 and x = (-5 - √63 * i) / 2

The equation (x+5)(x+6) = 2(3x+4) has two solutions, both of which are complex numbers: x = (-5 + √63 * i) / 2 and x = (-5 - √63 * i) / 2.