An equation in the form x² = k can be solved as x = ±√k. This method can also be used after transforming an equation into the form (x + p)² = q.
📘 Example ①
Solve x² = 12.
Answer:x = ±√12 = ±2√3
Solve x² = 12.
Answer:x = ±√12 = ±2√3
📘 Example ②
Solve (x − 3)² = 5.
Answer:x − 3 = ±√5 → x = 3 ± √5
Solve (x − 3)² = 5.
Answer:x − 3 = ±√5 → x = 3 ± √5
💡 Key Points
- x² = k → x = ±√k（k ≥ 0）
- (x + p)² = q → x = −p ± √q
Practice Problems
- Solve x² = 18.
- Solve (x + 2)² = 9.
Answers and Explanations
- Answer:x = ±3√2.
- Answer:x = 1, −5. x + 2 = ±3 → x = 1 or −5.