1. The user seems to be asking for preliminary formulas and conjectures along with their solutions and SOP (Standard Operating Procedure). 2. Since the question is unclear or incomplete, I will provide a simple, general explanation of how to approach formulas and conjectures in math. 3. A formula is an equation that shows the relationship between variables, e.g., the area of a rectangle $A = l \times w$. 4. A conjecture is a mathematical statement believed to be true based on observations, but not yet proven. 5. To solve any formula or explore a conjecture, you plug in values or manipulate expressions step-by-step using algebraic rules. 6. The SOP involves understanding the problem, identifying known data and unknowns, applying appropriate formulas/theorems, working through calculations, and verifying results. 7. If you have a specific formula or conjecture in mind, please provide it for a detailed explanation and solution.