# Completing the Square

- Author:
- cprystalski, Irina Boyadzhiev

- Topic:
- Square

This applet demonstrates a geometric interpretation of the method of completing the square. The construction was first described during the 9 .

^{th}century by the great Persian mathematician Al-Khwarizmi in his book*The Compendious Book on Calculation by Completion and Balancing*. We consider the equation1. Slowly move the slider to see

- an x-by-x square with area x
^{2 } - a 10-by-x rectangle with area 10x.

^{2}+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 x^{2}+10x, we add 5^{2}to get:**x**^{2}+10x+25