Resolviendo la ecuación cuadrática $x^2-5x+6=0$ por factorización

Overview

A brief walkthrough of solving the quadratic equation $x^2-5x+6=0$ using factorization. Viewers see the original equation, its factorized form, the two linear factors set to zero, and the final solutions highlighted.

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Phases

#	Phase Name	Duration	Description
1	Intro & Equation	~4 s	Title "Resolviendo la ecuación:" fades in at the top, then the original equation $x^2-5x+6=0$ writes in the centre.
2	Factorización	~6 s	Text "Factorizamos el trinomio:" appears below the equation, then the equation transforms into its factorized form $(x-2)(x-3)=0$.
3	Separar factores	~6 s	The factor‑text fades out, a new label "Igualamos cada factor a cero:" slides in from the left, and the two linear equations $x-2=0$ and $x-3=0$ write side‑by‑side beneath the factorized expression.
4	Resultado final	~6 s	Each linear equation morphs into its solved form $x_{1}=2$ and $x_{2}=3$ (colored yellow). A brief "indicate" pulse emphasizes each solution.
5	Outro	~3 s	A small caption "Solución completa" fades in at the bottom, then the whole scene holds for a moment before fading out.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │  ← Title / section label
├─────────────────────────────────────────────┤
│                 MAIN AREA                   │  ← Equation, factorization, solutions
├─────────────────────────────────────────────┤
│                BOTTOM AREA                  │  ← Caption / source note
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	"Resolviendo la ecuación:" (large, bold)	Fades in at the start of Phase 1, stays visible throughout
Main	All mathematical objects: original equation, factorized form, linear factors, solved values; also the short explanatory texts that appear in Phases 2‑4	Central focus; texts appear/disappear as described in each phase
Bottom	Small caption "Solución completa" (optional source note)	Fades in during Phase 5, uses a semi‑transparent background for readability

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Assets & Dependencies

• Fonts: LaTeX math font (default Manim), sans‑serif for textual labels.
• Colors:
  • Primary text: white on dark background (or black on light, depending on theme).
  • Highlighted solutions: YELLOW.
  • Background: solid dark navy (or light gray) to ensure contrast.
• External assets: None.
• Manim version / plugins: Manim Community Edition 0.18 (or later). No additional plugins required.

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Notes

• All fades, writes, and transforms should use Manim’s default easing for smoothness.
• The explanatory texts (e.g., "Factorizamos el trinomio:") must have an opaque background rectangle (e.g., semi‑transparent black) to keep them legible over the equation.
• The "Indicate" pulse on the final solutions should be brief (≈0.8 s) and repeat once per solution.
• Total runtime ≈ 25 seconds, well within the 30‑second guideline.