The Greeks had a method of completing the square geometrically in which they literally changed a figure into a square. For example, to complete the square for x² + 6x, we begin with a square of side x, as in the figure on the top. We add three rectangles of width 1 to the right side and the bottom to get a region with area x² + 6x. To fill in the corner (complete the square), we must add nine 1-by-1 squares as shown.

What is the area of the new “complete” square?

Transcribed Image Text:

X x + 3 X x + 3