Completing the square

A video visualizing how completing the square works.

In elementary algebra, Completing the square is a technique in evaluating quadratic expressions. The technique is about converting the quadratic expression in the standard form $ax^{2}+bx+c$, into the vertex form $a(x-h)^{2}+k$.

History

The technique of completing the square was known in the Old Babylonian Empire.

Muhammad ibn Musa Al-Khwarizmi, a famous polymath who wrote the early algebraic treatise Al-Jabr, used the technique of completing the square to solve quadratic equations.