The discussion focuses on the method of completing the square for the multivariable function defined by the equation x² + y² + 2xy - 2x - 2y + 43 = 0. The user successfully transforms the equation into the form ((x + y) - 1)² + 42, demonstrating a clear understanding of the technique. The user seeks alternative methods for completing the square, indicating a desire for optimization or simplification. However, the response suggests that the presented method is already efficient and aesthetically pleasing.
PREREQUISITESStudents studying algebra, mathematics educators, and anyone interested in enhancing their skills in solving multivariable equations through completing the square.
That looks plenty "nice" to me !pondzo said:Homework Statement
completing the squares; ## x^2+y^2+2xy-2x-2y+43 = 0##
The Attempt at a Solution
I did it as follows, but i would like to know if there is a different 'nicer' method to complete it;
## x^2 + y^2 + 2xy − 2x − 2y + 43 ##
## = (x + y)^2 − 2x − 2y + 43 ##
## = (x + y)^2 − 2(x + y) + 43 ##
## = (x + y)^2 − 2(x + y) + 1 + 42 ##
## = ((x + y) − 1)^2 + 42 ##