Given, x² + x + 1 = 0

=> x = {-1 ± √(1 - 4*1*1)}/2       [when ax² + bx + c = 0, then x = {-b ± √(b² - 4*a*c)}/2a]

=> x = {-1 ± √(1 - 4)}/2

=> x = {-1 ± √(-3)}/2

=> x = {-1 ± √3 * √(-1)}/2    {since i = √(-1)}

=> x = {-1 ± i√3}/2