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.
The blue area is therefore: x2+10x. 2. Keep slowly sliding. Next we divide the rectangle into two parts, and move the parts, getting ready to form a SQUARE. 3. Keep slowly sliding. We are COMPLETING THE SQUARE (geometrically, instead of algebraically.) The orange square completes our large square.
4. Thus, to COMPLETE THE SQUARE for x2+10x, we add 52 to get: x2+10x+25