To find the solutions of the quadratic equation x² + 2x + 2 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In this case, the coefficients are: a = 1, b = 2, and c = 2.
First, we calculate the discriminant (b² – 4ac):
Discriminant = 2² – 4(1)(2) = 4 – 8 = -4
Since the discriminant is negative (-4), this indicates that the solutions are complex numbers. Now, we can plug the values into the quadratic formula:
x = (-2 ± √(-4)) / 2(1)
This simplifies to:
x = (-2 ± 2i) / 2
Finally, simplifying that gives:
x = -1 ± i
Thus, the solutions to the equation x² + 2x + 2 = 0 are:
x = -1 + i and x = -1 – i.