in Babylonian times (around 4000 years ago) there is evidence from a number of tablets that there were techniques used that involved forming and solving quadratic equations

this study seems to have arisen and developed in connection with a need to divide up land fairly (for inheritance purposes)

one of the shapes regularly involved was the right trapezium

suppose you have a piece of land that you know the area of

you know about the slope of a line, translated as a 'feed'

you want to find the width of a strip

find the area of the whole rectangle

deduct the area of the right-angled triangle (the height of which is found from the known 'feed')

and you are left with a known area 'R' (e.g one fifth of a total area)

so a quadratic equation was created (born) to find the value of 's'

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