To solve the quadratic equation x² + 7x + 5, we can use the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / (2a)
In this equation, a = 1 (the coefficient of x²), b = 7 (the coefficient of x), and c = 5 (the constant term). Plugging in these values:
a = 1, b = 7, c = 5
First, we calculate the discriminant (b² – 4ac):
Discriminant = 7² – 4(1)(5) = 49 – 20 = 29
Now that we have the discriminant, we can substitute all values into the quadratic formula:
x = (−7 ± √29) / (2 × 1)
This simplifies to:
x = (−7 ± √29) / 2
Thus, the solutions for the equation x² + 7x + 5 are:
x = (−7 + √29) / 2 and x = (−7 − √29) / 2