Answer:
x = -1 ±2i sqrt(2)
Explanation:
x^2 + 2x + 9 = 0.
I will solve by completing the square
Subtract 9 from each side
x^2 + 2x + 9-9 = 0 -9
x^2 + 2x =- 9
Add (2/2) ^2 = 1^2 = 1 to each side
x^2 + 2x +1 =- 9+1
x^2 + 2x +1 =- 8
(x+1)^2 = -8
Take the square root of each side
sqrt((x+1)^2) =± sqrt(-8)
x+1 = ±sqrt(-8)
Subtract 1 from each side
x+1-1 = -1 ±sqrt(-8)
x = -1 ±sqrt(-8)
We can simplify sqrt(-8)
sqrt(-8) = sqrt(-1) sqrt(8) = i sqrt(4) sqrt(2) = 2i sqrt(2)
x = -1 ±2i sqrt(2)