Completing the Square
This applet demonstrates a geometric interpretation of the method of completing the square. The construction was first described during the 9th century by the great Persian mathematician Al-Khwarizmi in his book The Compendious Book on Calculation by Completion and Balancing. We consider the equation .
1. Slowly move the slider to see
- an x-by-x square with area x2
- a 10-by-x rectangle with area 10x.
4. Thus, to COMPLETE THE SQUARE for x2+10x, we add 52 to get: x2+10x+25