If x² = 49 and x < 0, then x =

## The reasoning The equation x² = 49 asks: "What number, when multiplied by itself, gives 49?" Two numbers work: 7 × 7 = 49 **and** (−7) × (−7) = 49. (Remember: negative times negative equals positive!) But here's the key — the question adds a **condition**: x < 0, meaning x must be negative. So even though both 7 and −7 satisfy x² = 49, only **−7** meets the requirement that x < 0. ## Why the wrong options tempt you **A) 7** — This is the "automatic" answer when you see √49. You forgot to check the condition x < 0. **C) 49** — Basic confusion. If x² = 49, then x ≠ 49. Test it: 49² = 2401, not 49. **D) −49** — You might think "negative answer needed" and just slap a minus sign on 49. But (−49)² = 2401, not 49. ## Quick takeaway Always read the full question — conditions like x < 0 or x > 0 tell you **which** solution to pick when there are multiple possibilities.