Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:**Question 2:**
What are the solutions to \((x - 3)^2 = -27\)?
**Explanation:**
To solve this equation, notice that the expression \((x - 3)^2\) represents a perfect square. A perfect square is always non-negative, meaning it cannot equal a negative number like \(-27\). Therefore, the equation \((x - 3)^2 = -27\) has no real solutions.
For further exploration, you can consider imaginary numbers where \(i^2 = -1\). This allows for solutions in the complex number system.
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