Final answer:
The quadratic equation v² + 7v + 4 = 0 is solved using the quadratic formula, which gives two solutions: v = (-7 + √33) / 2 and v = (-7 - √33) / 2.
Step-by-step explanation:
To solve the quadratic equation v² + 7v + 4 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c from the equation, which is in the standard form av² + bv + c = 0. Here, a = 1, b = 7, and c = 4.
The quadratic formula is given by:
v = (-b ± √(b² - 4ac)) / (2a)
Plugging our values into the formula:
v = (-(7) ± √((7)² - 4(1)(4))) / (2(1))
v = (-7 ± √(49 - 16)) / 2
v = (-7 ± √33) / 2
Therefore, the solutions to the equation are:
v = (-7 + √33) / 2 and v = (-7 - √33) / 2