Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(x − 2)2 = 25

To solve the equation \((x - 2)^2 = 25\), we will follow these steps:

### Step 1: Take the square root of both sides.
\[
\sqrt{(x - 2)^2} = \pm \sqrt{25}
\]
\[
x - 2 = \pm 5
\]
This gives us two cases to consider:

### Step 2: Solve for \(x\).
1. \(x - 2 = 5\)
\[
x = 5 + 2 = 7
\]
2. \(x - 2 = -5\)
\[
x = -5 + 2 = -3
\]

### Step 3: List the exact solutions.
The exact solutions are:
\[
x = 7 \quad \text{or} \quad x = -3
\]

### Step 4: Provide approximate solutions.
Since the solutions are already exact integers, the approximations are the same:
\[
x \approx 7.00 \quad \text{or} \quad x \approx -3.00
\]

Would you like further details on this process, or do you have any questions?

### 5 Related Questions:
1. How do you solve equations involving square roots with more complex expressions?
2. What happens if the value under the square root is negative?
3. Can you use factoring to solve quadratic equations like this one?
4. How would this process change if we had an inequality instead of an equation?
5. What are the properties of square roots and how do they apply here?

**Tip:** Always remember to consider both the positive and negative roots when taking the square root of both sides in an equation.

Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places. (x − 2)^2 = 25

Learn how to solve the equation (x - 2)^2 = 25 by extracting the square roots. This problem covers key algebraic concepts, including the square root property and how to solve quadratic equations. Suitable for students in Grades 7-9.

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