Answer :
Answer:
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)
Answer:
x equals negative 1 plus or minus 2 I square root of 2.
Step-by-step explanation:
Given equation is :
[tex]x^{2}+2x+9=0[/tex]
The quadratic equation formula is :
[tex]x_1_,_2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Here a = 1, b = 2 and c = 9
Putting the values, we get;
[tex]x=-1+2\sqrt{2} i[/tex] and [tex]x=-1-2\sqrt{2} i[/tex]
Therefore, the correct answer is : x equals negative 1 plus or minus 2 I square root of 2.