Which strategy is the most appropriate strategy to solve (x−1)^2=9 ?

To solve the equation \((x - 1)^2 = 9\), the most appropriate strategy is to **apply the square root property**. Here's the step-by-step process:

### Step 1: Apply the square root property
The square root property states that if \(a^2 = b\), then \(a = \pm \sqrt{b}\).

\[
(x - 1)^2 = 9 \quad \Rightarrow \quad x - 1 = \pm \sqrt{9}
\]

### Step 2: Simplify the square root
\[
x - 1 = \pm 3
\]

### Step 3: Solve for \(x\)
Now, split the equation into two cases:
1. \(x - 1 = 3\)
   \[
   x = 3 + 1 = 4
   \]
   
2. \(x - 1 = -3\)
   \[
   x = -3 + 1 = -2
   \]

### Step 4: Final solution
The solutions are:
\[
x = 4 \quad \text{or} \quad x = -2
\]

Thus, the equation \((x - 1)^2 = 9\) has two solutions: \(x = 4\) and \(x = -2\).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you solve a quadratic equation by factoring?
2. What are the general methods to solve a quadratic equation?
3. How can you check if a solution to an equation is correct?
4. What is the geometric interpretation of \((x - 1)^2 = 9\)?
5. How do you solve equations that involve higher powers, like \((x-1)^3 = 9\)?

**Tip**: Always check your solutions by substituting them back into the original equation!

Which strategy is the most appropriate strategy to solve (x−1)^2=9?

Explore how to solve the quadratic equation (x−1)^2 = 9 using the square root property. This step-by-step solution covers important algebraic concepts and explains how to simplify and solve for x. Suitable for students in Grades 8-10.

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