Need help with a practice Polynomial Question? A little confused

x^2  - 5x  - 8  = 0    add 8 to both sides

x^2  - 5x   = 8

Take  1/2 of 5  = 5/2....square it  = 25/4    .....add to both sides

x^2 - 5x  + 25/4  =  8 + 25/4       factor the left side, simpliify the right

(x - 5/2)^2  =  57/4      take both roots

x - 5/2  =  ± √ [ 57 / 4 ]

x - 5/2  = ± √57 / 2      add 5/2 to both sides

x  = 5/2  + √57/ 2          or   x  =  5/2   - √57 / 2