(x-1)^2=9

less than a minute read Jun 17, 2024
(x-1)^2=9

Solving the Equation (x - 1)^2 = 9

This article will guide you through the steps of solving the equation (x - 1)^2 = 9.

Understanding the Equation

The equation involves a squared term, (x - 1)^2, which means the expression (x - 1) is multiplied by itself.

Solving for x

  1. Take the square root of both sides:

    √(x - 1)^2 = ±√9

    This gives us two possible solutions because the square root of a number can be positive or negative.

  2. Simplify:

    x - 1 = ±3

  3. Isolate x:

    x = 1 ± 3

  4. Solve for the two possible values of x:

    • x = 1 + 3 = 4
    • x = 1 - 3 = -2

Conclusion

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

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