The given equation involves a power of the variable. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
(x − 2)2 = 5

To solve the equation \((x - 2)^2 = 5\) for all real solutions, follow these steps:

1. **Take the square root of both sides** to eliminate the square:
   \[
   \sqrt{(x - 2)^2} = \sqrt{5}
   \]

2. **Simplify** the equation:
   \[
   x - 2 = \pm \sqrt{5}
   \]
   This gives two possible equations:
   \[
   x - 2 = \sqrt{5} \quad \text{or} \quad x - 2 = -\sqrt{5}
   \]

3. **Solve for \(x\)** in both cases:
   \[
   x = \sqrt{5} + 2
   \]
   \[
   x = -\sqrt{5} + 2
   \]

So, the real solutions are:
\[
\boxed{2 + \sqrt{5}, 2 - \sqrt{5}}
\]

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve quadratic equations by completing the square?
2. What are the steps to solve equations involving higher powers of a variable?
3. How do you determine if a quadratic equation has real or complex solutions?
4. What is the quadratic formula, and how is it used?
5. Can you explain how to solve equations involving absolute values?

**Tip:** When solving equations involving squares, always consider both the positive and negative roots.

Discover how to find all real solutions of the equation (x − 2)^2 = 5. This problem involves equations with powers of variables and requires understanding square roots and solving for variables. Suitable for advanced high school students.

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