Answer:
x = - 1 ± i [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
3x² = - 12 - 6x ( add 6x to both sides )
3x² + 6x = - 12 ( divide through by 3 )
x² + 2x = - 4
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1 = - 4 + 1
(x + 1)² = - 3 ( take the square root of both sides )
x + 1 = ± [tex]\sqrt{-3}[/tex] = ± i [tex]\sqrt{3}[/tex] ( subtract 1 from both sides )
x = - 1 ± i [tex]\sqrt{3}[/tex]
