(x-1)(x+1)-9=5x

3 min read Jun 17, 2024

Solving the Equation: (x-1)(x+1)-9 = 5x

This article will guide you through the steps to solve the equation (x-1)(x+1)-9 = 5x. We'll use algebraic techniques to simplify and isolate the variable 'x'.

Step 1: Expand the Left Side

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

(x-1)(x+1) = x² - 1

Now, the equation becomes: x² - 1 - 9 = 5x

Step 2: Simplify the Equation

Combining the constants on the left side, we get: x² - 10 = 5x

Step 3: Move all Terms to One Side

To solve for x, we need to have all terms on one side of the equation. Subtract 5x from both sides: x² - 5x - 10 = 0

Step 4: Solve the Quadratic Equation

The equation is now in the standard quadratic form (ax² + bx + c = 0). We can solve this using the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

In this case, a = 1, b = -5, and c = -10. Substitute these values into the quadratic formula:

x = [5 ± √((-5)² - 4 * 1 * -10)] / (2 * 1)

x = [5 ± √(85)] / 2

Therefore, the solutions for the equation are:

x = (5 + √85) / 2 and x = (5 - √85) / 2

Conclusion

By following these steps, we have successfully solved the equation (x-1)(x+1)-9 = 5x. The solutions are x = (5 + √85) / 2 and x = (5 - √85) / 2. Remember to always check your solutions by substituting them back into the original equation to ensure they are valid.