SOLUTION: Use the Babylonian approach to solve x^2+ 6x = 16

Question 621183: Use the Babylonian approach to solve x^2+ 6x = 16
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The Babylonian method is nothing more than using geometric figures to perform the operation of completing the square.

Factor the LHS:

This equation can be represented geometrically by a rectangle that measures

.

The rectangle described can be divided into two parts, one that is a square that mesures

on each side, and the other a

rectangle.

If the

rectangle is further divided in half to form two

rectangles, then one of those smaller rectangles can be moved to either adjacent side of the

square.

The figure that results is a figure that has an area of 16 and is almost a square in shape except for a

square in one corner. Adding that square adds an area of 9 to the overall figure, giving the overall figure an area of 25. We can describe this algebraically by summing the areas of the four pieces that make the overall square:

Combining terms

We recognize a perfect square trinomial in the LHS, hence:

Taking the root:

Hence

Though I suspect the geometrically minded Babylonians may well have discarded the negative root as non-sensical in a world where quantities are considered measures of length.

John

My calculator said it, I believe it, that settles it

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