To find the solutions for the quadratic equation x² + 5x + 8 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In our case, the coefficients are:
- a = 1
- b = 5
- c = 8
Now, we can calculate the discriminant (b² – 4ac):
b² – 4ac = 5² – 4(1)(8) = 25 – 32 = -7
Since the discriminant is negative (-7), this means that the quadratic equation has no real solutions but does have two complex solutions. We can proceed to find those solutions:
x = (-5 ± √(-7)) / 2(1)
This simplifies to:
x = (-5 ± i√7) / 2
Therefore, the solutions to the equation x² + 5x + 8 = 0 are:
x = -2.5 + (i√7)/2 and x = -2.5 – (i√7)/2