AT-OEMO-REG 2000 Problem 2

For any real number $a$ , find all real numbers $x$ that satisfy the following equation. $(2x + 1)^4 + ax(x + 1) - \frac{x}{2}= 0$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.