Step-by-step explanation:
x² + 6x + 9 = 2
(x + 3)² = 2
x + 3 = ±sqrt(2)
x = -3 ± sqrt(2)
so, B and D are correct.
control :
(-3 + sqrt(2))² + 6(-3 + sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) - 18 + 6sqrt(2) + 9 = 2
2 = 2
correct
(-3 - sqrt(2))² + 6(-3 - sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) - 18 - 6sqrt(2) + 9 = 2
2 = 2
correct
(3 + sqrt(2))² + 6(3 + sqrt(2)) + 9 = 2
9 + 2 + 6sqrt(2) + 18 + 6sqrt(2) + 9 = 2
38 + 12sqrt(2) = 2
wrong.
(3 - sqrt(2))² + 6(3 - sqrt(2)) + 9 = 2
9 + 2 - 6sqrt(2) + 18 - 6sqrt(2) + 9 = 2
38 - 12sqrt(2) = 2
wrong.
