To solve the quadratic equation x² + 5x + 3 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 1, b = 5, and c = 3. First, we need to calculate the discriminant (b² – 4ac):
b² – 4ac = 5² – 4(1)(3) = 25 – 12 = 13.
Now, we can substitute the values into the quadratic formula:
x = (-5 ± √13) / 2(1)
This gives us two possible solutions for x:
x₁ = (-5 + √13) / 2 and x₂ = (-5 – √13) / 2.
These are the two roots of the quadratic equation. The value of √13 is approximately 3.605, so we can calculate the numerical solutions:
x₁ ≈ (-5 + 3.605) / 2 ≈ -0.6975
x₂ ≈ (-5 – 3.605) / 2 ≈ -4.3025
Thus, the solutions to the equation x² + 5x + 3 = 0 are:
- x ≈ -0.6975
- x ≈ -4.3025