Completing the square beyond quadratic equations

Xicheng Peng

doi:10.1080/00255572.2026.2696530

July 13, 2026The Mathematical Gazette

Completing the square beyond quadratic equations

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Key Points

The study aims to explore real solutions of a specific polynomial equation using the method of completing the square.
Analyzes the equation x²−2xsin(πx²)+1=0 from a mathematical competition context.
Utilizes techniques of completing the square beyond traditional applications in quadratic equations.
Identified real solutions through advanced methods of completing the square technique.
Provided novel insights into handling trigonometric and polynomial interactions.

Implication

Explores real solutions for a complex equation using advanced methods, indicating a novel approach.

Abstract

A problem from the 1956 Beijing Mathematics Competition asks for the real solutions of x2−2xsin⁡(πx2)+1=0. A commonly circulated solution treats the expression formally as a quadratic in x, lead...

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Cite This Study

Xicheng Peng (2026) studied this question.

synapsesocial.com/papers/6a57242188b21df875480946 https://doi.org/10.1080/00255572.2026.2696530

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Completing the square beyond quadratic equations

Key Points

Implication

Abstract

Discussion

Cite This Study

Completing the square beyond quadratic equations

Key Points

Implication

Abstract

Discussion

Cite This Study

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