(x+9)(x+1)=x(x+8)-1

2 min read Jun 17, 2024

Solving the Equation (x+9)(x+1) = x(x+8) - 1

This article will guide you through solving the equation (x+9)(x+1) = x(x+8) - 1. We will use algebraic manipulation to simplify the equation and arrive at a solution for x.

1. Expanding both sides of the equation

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

Left side: (x+9)(x+1) = x² + 10x + 9
Right side: x(x+8) - 1 = x² + 8x - 1

Now our equation looks like this: x² + 10x + 9 = x² + 8x - 1

2. Simplifying the equation

Next, we can simplify the equation by subtracting x² from both sides. This will cancel out the quadratic term, leaving us with a linear equation.

10x + 9 = 8x - 1

3. Isolating the variable

Now, we need to isolate x on one side of the equation. We can do this by subtracting 8x from both sides:

2x + 9 = -1

Then, subtract 9 from both sides:

2x = -10

4. Solving for x

Finally, we can solve for x by dividing both sides by 2:

x = -5

Conclusion

Therefore, the solution to the equation (x+9)(x+1) = x(x+8) - 1 is x = -5.