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Caleb is solving the equation \( x = \sqrt{x + 2} + 7 \). His steps show that he squared both sides of the equation, which introduces the potential for **extraneous solutions**. This happens because squaring both sides of an equation can introduce solutions that do not satisfy the original equation.

Thus, **it is necessary** for Caleb to check his answers for extraneous solutions, as not all solutions to the squared equation might be valid for the original equation involving the square root.

The correct answer is:
- **A) Yes**

Would you like further details on how to handle extraneous solutions or any other questions? 

Here are some related questions:
1. Why do squaring both sides of an equation potentially introduce extraneous solutions?
2. How can Caleb check if a solution is extraneous?
3. What are the next steps Caleb would take after reaching \( x^2 - 14x + 49 = x + 2 \)?
4. What are common methods to solve square root equations?
5. How does one verify a solution in a radical equation?

**Tip:** Always substitute solutions back into the original equation to ensure they work, especially when dealing with square roots or any operation that could introduce extraneous solutions.

Caleb is solving the following equation for x: x = √(x + 2) + 7. Is it necessary for Caleb to check his answers for extraneous solutions?

Learn how to solve the equation x = √(x + 2) + 7, and understand why it's necessary to check for extraneous solutions when squaring both sides. This problem covers key algebra concepts and is suitable for students in Grades 9-10.

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