When decimals, fractions, or parentheses are included, simplify the equation before solving it.
📘 Example ① (Parentheses)
Solve (x + 1)(x − 3) = 5.
Answer:Expand: x² − 2x − 3 = 5 → x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0 → x = 4, −2
Solve (x + 1)(x − 3) = 5.
Answer:Expand: x² − 2x − 3 = 5 → x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0 → x = 4, −2
📘 Example ② (Fractions)
Solve x²/2 − x − 1 = 0.
Answer:×2: x² − 2x − 2 = 0 → x = (2 ± √12) / 2 = 1 ± √3
Solve x²/2 − x − 1 = 0.
Answer:×2: x² − 2x − 2 = 0 → x = (2 ± √12) / 2 = 1 ± √3
💡 Key Points
- Expand → transpose terms → put the equation in standard form (right side=0) before solving
- For fractions, multiply the entire equation by the LCM of the denominators
Practice Problems
- Solve (x + 3)² = 16.
- Solve (x − 1)(x + 4) = −4.
Answers and Explanations
- Answer:x = 1, −7. x + 3 = ±4.
- Answer:x = 0, −3. Expand: x² + 3x − 4 = −4 → x² + 3x = 0 → x(x+3)=0.