Completing the square, literally
An x-by-x square is joined by two strips of width 3/2, representing the algebraic expression x squared plus 3x. The animation reveals a missing corner piece of area 9/4 needed to form a perfect square. Filling that gap shows why x squared plus 3x equals (x plus 3/2) squared minus 9/4, giving students a geometric reason behind the completing-the-square technique used in solving quadratics.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
x² + 3x drawn as an x-by-x square plus two strips of width 3/2. The strips leave a missing corner of area 9/4. Filling it completes a perfect square of side x + 3/2, which is exactly why x² + 3x equals (x + 3/2)² minus 9/4.
Make the next one in this series
- Show completing the square for x² + bx with a general coefficient b using the same strip method
- Animate solving a quadratic equation step by step using the completed square form
- Compare completing the square visually to deriving the quadratic formula algebraically
