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The equation you provided is:

\[
(x - 1)^2 = 3
\]

To solve for \(x\), follow these steps:

### Step 1: Take the square root of both sides
\[
\sqrt{(x - 1)^2} = \pm \sqrt{3}
\]

This simplifies to:
\[
x - 1 = \pm \sqrt{3}
\]

### Step 2: Solve for \(x\)
Now, isolate \(x\) by adding 1 to both sides:
\[
x = 1 \pm \sqrt{3}
\]

So, the solutions are:
\[
x = 1 + \sqrt{3} \quad \text{or} \quad x = 1 - \sqrt{3}
\]

These are the two possible values of \(x\).

Would you like a deeper explanation or have any further questions? Here are some related questions for further practice:

1. What are the approximate decimal values of \( 1 + \sqrt{3} \) and \( 1 - \sqrt{3} \)?
2. How do you solve equations involving other roots like cube roots?
3. What happens if the equation is \( (x - 1)^2 = -3 \)?
4. How can you factor quadratic expressions like \( (x - 1)^2 \) when expanded?
5. What are some applications of quadratic equations in physics or engineering?

**Tip:** Always remember that taking the square root introduces both the positive and negative roots, which is why you have the \( \pm \) symbol in the solution.

Learn how to solve the quadratic equation (x - 1)^2 = 3 using square roots and algebraic techniques. This detailed step-by-step guide is suitable for students in Grades 9-10.

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