1. One solution of al-Khwarizmi Solve + 12x = 85 by drawing the square shown. The area of the four white rectangles and the yellow square is r + 12x . We then set this expression equal to 85 to get the equ r² + 12r = 85. If we add the four blue squares, we will have a larger square of known area. Complete the solution. 3 3 Area = x? Area = 3x each with its own rule. Thomas Harriot (1560-1621) introduced the method of factoring to obtain solutions, and François Viète (1540 – 1603) introduced a method that is essentially completing the square.
1. One solution of al-Khwarizmi Solve + 12x = 85 by drawing the square shown. The area of the four white rectangles and the yellow square is r + 12x . We then set this expression equal to 85 to get the equ r² + 12r = 85. If we add the four blue squares, we will have a larger square of known area. Complete the solution. 3 3 Area = x? Area = 3x each with its own rule. Thomas Harriot (1560-1621) introduced the method of factoring to obtain solutions, and François Viète (1540 – 1603) introduced a method that is essentially completing the square.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.4: The Addition-or-subtraction Method
Problem 7P
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Transcribed Image Text:1. One solution of al-Khwarizmi Solve r + 12x = 85 by drawing the square shown. The area of the four white rectangles and the yellow square is r² + 12x. We then set this expression equal to 85 to get the equation
12 + 12r = 85 . If we add the four blue squares, we will have a larger square of known area. Complete the solution.
3
3
Area = x?
3
Area = 3x
3
each with its own rule. Thomas Harriot (1560-1621) introduced the method of factoring to obtain solutions, and François Viète (1540 – 1603) introduced a method that is essentially completing the square.
Until modern times it was usual to neglect the negative roots (if there were any), and equations involving square roots of negative quantities were regarded as unsolvable until the 1500 s
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