Answer: -3 and -17
Explanation:
When completing the square we add and subtract
in the form ax² + bx + c.

x² - 6x - 8 = (x - __)² - __
(x² - 6x) - 8 = (x - __)² - __
(x² - 6x + 9) - 8 - 9 = (x - __)² - __
(x - 3)² - 17 = (x - __)² - __
The blanks are 3 and 17.