(x+1)(2x+8)=(x+7)(x+3)

3 min read Jun 16, 2024

Solving the Equation: (x+1)(2x+8) = (x+7)(x+3)

This article will guide you through the steps of solving the equation (x+1)(2x+8) = (x+7)(x+3). We will use algebraic manipulation to isolate the variable x and find its value(s).

Step 1: Expand both sides of the equation

First, we need to expand both sides of the equation by multiplying the terms within the parentheses.

(x+1)(2x+8) = (x+7)(x+3)

Left Side: (x+1)(2x+8) = 2x² + 8x + 2x + 8 = 2x² + 10x + 8
Right Side: (x+7)(x+3) = x² + 3x + 7x + 21 = x² + 10x + 21

Now, our equation becomes:

2x² + 10x + 8 = x² + 10x + 21

Step 2: Combine like terms

Next, we need to combine like terms on both sides of the equation. In this case, we can subtract x² and 10x from both sides.

2x² + 10x + 8 - x² - 10x = x² + 10x + 21 - x² - 10x

This simplifies to:

x² + 8 = 21

Step 3: Isolate the x² term

To isolate the x² term, we can subtract 8 from both sides of the equation.

x² + 8 - 8 = 21 - 8

This leaves us with:

x² = 13

Step 4: Solve for x

Finally, to solve for x, we need to take the square root of both sides of the equation.

√x² = ±√13

Therefore, the solutions to the equation are:

x = √13 and x = -√13

Conclusion

By carefully following the steps of algebraic manipulation, we successfully solved the equation (x+1)(2x+8) = (x+7)(x+3) and found the two solutions: x = √13 and x = -√13.