Question

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

Answer 1

x equals negative 1 plus or minus 2 I square root of 2.

Explanation:

Given equation is :

`x^(2)+2x+9=0`

The quadratic equation formula is :

`x_1_,_2=\frac{-b+-\sqrt{b^(2)-4ac } }{2a}`

Here a = 1, b = 2 and c = 9

Putting the values, we get;

`x=-1+2√(2) i` and
`x=-1-2√(2) i`

Therefore, the correct answer is : x equals negative 1 plus or minus 2 I square root of 2.

Answer 2

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)