I need to find an unknown quantity using al-Khwarizmi algebra, this is the problem: "I divide 10 units into a quantity and a remaining part, so the sum of the squares of the two portions is 58 units." can someone help me out with this one??

You divide the 10 units into 7 and 3

(7 * 7) + (3 * 3 )
= 49 + 9
= 58

Hello charls

Although the previous post is correct, it does not answer your question on HOW to do it.
You have 10 figure units, so you also have the 10 amounts of their squares.
You take the amount of the given squares (58) and find which two squares from your list of 10 units add up to 58.
You find that only numbers 49 and 9 add up to 58, so the original figure units are V49 and V9 = 7 + 3.

If you would have 68 squares, you find that this is 64 + 4, so the original figure units are V64 + V4 = 8 + 2.