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The equation provided is \( x^2 = 45 \), where \( x \) is a real number. To solve for \( x \), follow these steps:

### Solution:

1. Start with the equation:
   \[
   x^2 = 45
   \]

2. Take the square root of both sides to solve for \( x \):
   \[
   x = \pm \sqrt{45}
   \]

3. Simplify \( \sqrt{45} \). Since \( 45 = 9 \times 5 \), we can factor out the square root of 9:
   \[
   x = \pm \sqrt{9 \times 5} = \pm \sqrt{9} \times \sqrt{5} = \pm 3\sqrt{5}
   \]

Thus, the simplified solution is:
\[
x = \pm 3\sqrt{5}
\]

### Final Answer:
\[
x = 3\sqrt{5} \quad \text{or} \quad x = -3\sqrt{5}
\]

Would you like further details or clarification?

Here are some related questions for further practice:

1. What is the general method for solving quadratic equations?
2. How do you simplify square roots involving products, like \( \sqrt{45} \)?
3. What are the properties of real numbers relevant to solving quadratic equations?
4. How would the solution change if the equation were \( x^2 = -45 \)?
5. What if \( x \) were required to be a positive number only?

**Tip:** Always check if the number under a square root can be simplified by factoring it into a perfect square times another number.

Solve x^2 = 45, where x is a real number. Simplify your answer as much as possible.

Learn how to solve x^2 = 45 by taking the square root of both sides and simplifying the result. This detailed step-by-step solution covers square root properties, simplifying radicals, and algebraic concepts. Suitable for Grades 7-9.

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