To find the approximate solutions of the quadratic equation 5x² + 7x + 1 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 5, b = 7, and c = 1.
First, we need to calculate the discriminant (b² – 4ac):
Discriminant = 7² – 4 × 5 × 1 = 49 – 20 = 29
Since the discriminant is positive, we will have two real and distinct solutions. Now, we can substitute the values into the quadratic formula:
x = (-7 ± √29) / (2 × 5)
This simplifies to:
x = (-7 ± √29) / 10
Now we find the square root of 29, which is approximately 5.385.
So we have:
x = (-7 + 5.385) / 10 ≈ -0.1615
and
x = (-7 – 5.385) / 10 ≈ -1.2385
Rounding these solutions to the nearest hundredth gives us:
x ≈ -0.16 and x ≈ -1.24.