how to go from u_{n+1} - u_n = 3((u_n)^2 - u_n) + 1 to 3(u_n - 1/2)^2 + 1/4 ?

[Shuai]

Hello

I have something like this :

Can someone explain to me how they went from

TO

Thank you very much

 

[stapel]

I have something like this:

. . . . .\(\displaystyle u_{n+1}\, -\, u_n\, =\, 3\, \left(u_n^2\, -\, u_n\right)\, +\, 1\, =\, 3\, \left(u_n\, -\, \dfrac{1}{2}\right)^2\, +\, \dfrac{1}{4}\)

Can someone explain to me how they went from

. . . . .\(\displaystyle 3\, \left(u_n^2\, -\, u_n\right)\, +\, 1\)

to

. . . . .\(\displaystyle 3\, \left(u_n\, -\, \dfrac{1}{2}\right)^2\, +\, \dfrac{1}{4}\)

What did you get, when you completed the square? (here)

 

[Shuai]

What did you get, when you completed the square? (here)

Yayyyyyyy !
it was so frustrating to understand since i'm french which took me a lot of time but I managed to make it
Thank you very much sir