Do you think we can complete a square using the tiles that represent the algebraic expression on the left?

Absolutely! Completing the square can easily be visualized using tiles! Imagine having square tiles for each x² term, rectangle tiles for each x term, and single tiles for constant numbers. By rearranging these tiles, you can form a perfect square. For example, to complete the square for x² + 6x, you’d add the appropriate number of tiles to create a larger square that visually represents (x + 3)². It’s like a puzzling game, making algebraic expressions feel more tangible! And, did you know that this technique not only works for linear equations but also extends to quadratic equations? Mathematicians in ancient civilizations, like the Babylonians, used similar methods to solve quadratic equations, essentially laying the groundwork for algebra. This "tiling" approach is a wonderful way to see the beauty and continuity of math through the ages—turning abstract concepts into something physical and visual makes it much easier to grasp!