The equation you provided is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 7, and c = 5. To find the solutions, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
Now, let’s plug in the values:
b² – 4ac = 7² – 4(1)(5) = 49 – 20 = 29
Next, we find the roots:
x = (-7 ± √29) / 2(1)
Calculating this gives us:
x₁ = (-7 + √29) / 2 and x₂ = (-7 – √29) / 2
Therefore, the solutions for the equation x² + 7x + 5 = 0 can be expressed as:
x₁ ≈ -0.195 and x₂ ≈ -6.805
In conclusion, the solutions of the equation are approximately -0.195 and -6.805.