Answer:
x = 3 ± i [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
x² - 6x + 12 = 0 ( subtract 12 from both sides )
x² - 6x = - 12
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 12 + 9
(x - 3)² = - 3 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{-3}[/tex] = ± i [tex]\sqrt{3}[/tex] ( add 3 to both sides )
x = 3 ± i [tex]\sqrt{3}[/tex]
