= History of completing the square
<Al-Khwarizmi> presented geometric completions of <squares> in his treatment of <quadratic equations>. His exposition used verbal instructions, positive lengths and <areas>, rather than the modern <algebraic notation> used here. The <area> assembly above illustrates the same principle with a different expression and arrangement. The modern <polynomial identity> also covers negative values of the <variable> and <roots of a polynomial> in the <complex numbers>, which need no interpretation as positive side lengths.<Al-Khwarizmi by John Joseph O'Connor and Edmund Frederick Robertson>[MacTutor, Abu Ja'far Muhammad ibn Musa Al-Khwarizmi: six standard equation forms, verbal algebra and geometric square completion]{ref}
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