Germany | Can you solve this? | Math Olympiad

[@walterwen2975]

Germany Math Olympiad: m³ + 5m = 42; m =?
m³ + 5m - 42 = 0, (m³ - 3³) + (5m - 15) = (m - 3)(m² + 3m + 9) + 5(m - 3) = 0
(m - 3)(m² + 3m + 14) = 0, m - 3 = 0 or m² + 3m + 14 = 0
m = 3 or m = (- 3 ± i√47)/2
Answer check:
m = 3: m³ + 5m = 3³ + 5(3) = 27 + 15 = 42; Confirmed
m = (- 3 ± i√47)/2, m² + 3m + 14 = 0: m² = - 3m - 14, m³ = - 3m² - 14m
m³ + 5m = (- 3m² - 14m) + 5m = - 3(m² + 3m) = (- 3)(- 14) = 42; Confirmed
Final answer:
m = 3, m = (- 3 + i√47)/2 or m = (- 3 - i√47)/2