(x-1)^2-9=0

less than a minute read Jun 17, 2024

Solving the Quadratic Equation: (x-1)² - 9 = 0

This article will guide you through the process of solving the quadratic equation (x-1)² - 9 = 0. We will utilize the following steps:

1. Simplifying the Equation

First, we simplify the equation by expanding the squared term:

(x-1)² - 9 = 0 x² - 2x + 1 - 9 = 0 x² - 2x - 8 = 0

2. Factoring the Quadratic Equation

Now, we factor the simplified quadratic equation:

(x - 4)(x + 2) = 0

3. Solving for x

Finally, we set each factor equal to zero and solve for x:

x - 4 = 0 => x = 4
x + 2 = 0 => x = -2

Conclusion

Therefore, the solutions to the quadratic equation (x-1)² - 9 = 0 are x = 4 and x = -2.

This method demonstrates a straightforward approach to solving quadratic equations by simplifying, factoring, and then solving for the unknown variable.