method of solving linear and quadratic equations

Al-Khwarizmi was a Persian mathematician. His book named Compendious Book on Calculation by Completion and Balancing was presenting the first systematic solution of linear and quadratic equations. His contributions to mathematics were so important that some mathematical terms were derivate from his name. For example, Algorism and algorithm come from “Algoritmi”, the Latin form of his name.

In his main work “The Compendious Book on Calculation by Completion and Balancing”, it explain the fundamental methods of “reduction” and “balancing” which refers to the transposition of subtracted terms to the other side of an equation. Al-Khwarizmi’s method of solving linear and quadratic equations is pretty simple. We are still using it in maths courses since high school. Basically, you have to firstly reduce the equation to one of six standard forms, which you surely can recognize, by dividing the coefficient of the square and using two operations (Al-jabr and Al-muqabala).

- Squares equal roots (ax2 = bx)
- Squares equal number (ax2 = c)
- Roots equal number (bx = c)
- Squares and roots equal number (ax2 + bx = c)
- Squares and number equal roots (ax2 + c = bx)
- Roots and number equal squares (bx + c = ax2)

Al-jabr: “The process of removing negative units, roots and squares from the equation by adding the same quantity to each side.”
Example: x^2 = 78x-7x^2 is reduce to 8^2 = 78x

Al-muqabala: “The process of bringing quantities of the same type to the same side of the equation.”
Example: x^2+10 = x+5 is reduced to x^2+5 = x

It is important to know that Al-Khwarizmi used text to present problems and solutions because algebra wasn’t existing in his time.


sumber dari: historyoflinearalgebra.weebly.com