Which optimization strategy did Al-Khwarizmi employ for solving quadratic equations using geometric algebra?

💡 Explanation

When solving quadratic equations, Al-Khwarizmi applied 'completing the square' because geometric algebra represented unknowns as areas and lengths; the method spatially manipulated these areas to form a complete square, directly revealing the solution. Therefore completing the square is the answer, rather than options (B), (C) or (D), which rely on symbolic manipulation or approximation uncommon in that era.

• Which characteristic of pre-Columbian chinampa agriculture maximized land use in swampy environments within Central Mexico?
• Which action enabled Mesopotamian bronze smiths to achieve superior hardness in their cast tools and weapons?
• Which agricultural modification enhances soil aeration in pre-Columbian chinampa cultivation?
• Which risk increased in 18th-century wooden sailing ships when hull sheathing changed from tarred felt to copper?
• Which mechanical consequence would result from prolonged use of Roman ballista siege engines with improperly heat-treated torsion springs?
• Which risk increased when cast bronze sickle blades replaced flint blades during the early Bronze Age harvests?