To find the solutions of the equation x² + 10x + 36 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, a = 1, b = 10, and c = 36. First, we calculate the discriminant:
Discriminant (D) = b² – 4ac = 10² – 4(1)(36) = 100 – 144 = -44
Since the discriminant is negative, this means that the equation has no real solutions. Instead, it has two complex solutions. We can find them using the quadratic formula:
x = (-10 ± √(-44)) / 2(1)
Now, simplifying further:
x = (-10 ± 2i√11) / 2
x = -5 ± i√11
Thus, the solutions to the equation x² + 10x + 36 = 0 are x = -5 + i√11 and x = -5 – i√11, which are both complex numbers.