Entendendo a equação do segundo grau através do completamento de quadrado

Abstract

This study aims to examine the application of the completing the square method as an alternative to the well-known Bhaskara formula for solving quadratic equations, with the aim of fostering more thoughtful and conceptually relevant learning. The research adopted a qualitative, bibliographical methodology, based on textbooks, academic articles, theses, and documents such as the National Common Curricular Base (BNCC). The assessment was conducted through the reading and interpretation of materials published since 2017, considering the historical context of the emergence of quadratic equations and the way the method is presented in teaching. The findings reveal that completing the square is often used simply as a preliminary step in deriving Bhaskara's formula, without being explored as an independent solution tactic. This perspective restricts students' understanding, encouraging the automatic application of formulas. It is concluded that the use of completing the square, when contextualized historically and employed pedagogically, can help improve logical reasoning, intellectual independence and in-depth understanding of the mathematical concepts covered.