Solve x^2 + 2x + 9 = 0.

x equals negative 2 plus or minus 4 i square root of 2
x equals negative 2 plus or minus 2 i square root of 2
x equals negative 1 plus or minus 4 i square root of 2
x equals negative 1 plus or minus 2 i square root of 2

x = -1 ±2i sqrt(2)

Step-by-step 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)

addition

step-by-step explanation: