Answer:
x = - 1 ± i[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
3s² + 8s = 2s - 9 ( subtract 2s - 9 from both sides )
3s² + 6s + 9 = 0
To complete the square
The coefficient of the s² term must be 1, so factor out 3 from 3s² + 6s
3(s² + 2s) + 9 = 0
add/subtract ( half the coefficient of the s- term )² to s² + 2s
3(s² + 2(1)s + 1 - 1) + 9 = 0
3(s + 1)² - 3 + 9 = 0
3(s + 1)² + 6 = 0 ( add 6 to both sides )
3(s + 1)² = - 6 ( divide both sides by 3 )
(s + 1)² = - 2 ( take the square root of both sides )
s + 1 = ± [tex]\sqrt{-2}[/tex] = ± i[tex]\sqrt{2}[/tex] ( subtract 1 from both sides )
s = - 1 ± i[tex]\sqrt{2}[/tex]
Thus
s = - 1 + i[tex]\sqrt{2}[/tex] , s = - 1 - i[tex]\sqrt{2}[/tex]
