Answer:
x = - 3 ± [tex]\sqrt{2}[/tex]
Step-by-step explanation:
x² + 6x + 7 = 0 ( subtract 7 from both sides )
x² + 6x = - 7
using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = - 7 + 9
(x + 3)² = 2 ( take square root of both sides )
x + 3 = ± [tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± [tex]\sqrt{2}[/tex]
