To solve the quadratic equation x² + 5x + 5 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 1, b = 5, and c = 5.
First, we need to calculate the discriminant (b² – 4ac):
Discriminant = 5² – 4(1)(5) = 25 – 20 = 5
Since the discriminant is positive (5), we will have two distinct real solutions. Now, we plug in the values into the quadratic formula:
x = (−5 ± √5) / 2
This gives us two solutions:
- x₁ = (−5 + √5) / 2
- x₂ = (−5 – √5) / 2
Thus, the solution set is:
{ (−5 + √5) / 2, (−5 – √5) / 2 }