Answer :

the square of a certain negative number is equal to 5 more than one half of that number
what is that number
let x be that number
thus        x²  =  x/2 + 5
               x² - x/2 - 5 =  0
               2x² - x -10 = 0
               (2x-5) (x + 2) =  0
                 x =  5/2    or    - 2
                 so the number is    - 2