(x-1)^2 =4

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-1)^2 = 4

This article will guide you through solving the equation (x-1)^2 = 4.

Understanding the Equation

The equation represents a quadratic equation in the form of (x-a)^2 = b, where 'a' and 'b' are constants. This form is particularly useful because it allows us to directly use the square root property.

Solving the Equation

1. Take the square root of both sides:

• √((x-1)^2) = ±√4
• Note: We include both positive and negative square roots because squaring both a positive and negative number results in a positive value.

2. Simplify:

• x - 1 = ±2

3. Isolate x:

• x = 1 ± 2

4. Solve for both possible values:

• x = 1 + 2 = 3
• x = 1 - 2 = -1

The Solution

Therefore, the solutions to the equation (x-1)^2 = 4 are x = 3 and x = -1.

Verifying the Solutions

To verify our solutions, we can substitute each value of x back into the original equation:

• For x = 3: (3 - 1)^2 = 2^2 = 4. This is true.
• For x = -1: (-1 - 1)^2 = (-2)^2 = 4. This is also true.

This confirms that our solutions are correct.

Conclusion

Solving the equation (x-1)^2 = 4 involves using the square root property, which simplifies the process of isolating x. By understanding the underlying principles and carefully following the steps, we arrive at two solutions: x = 3 and x = -1.