To find the solutions for the quadratic equation 2x² + 16x + 50 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 2, b = 16, and c = 50. We start by calculating the discriminant (b² – 4ac):
b² = 16² = 256
4ac = 4 * 2 * 50 = 400
Now, we calculate the discriminant:
Discriminant = 256 – 400 = -144
Since the discriminant is negative, this means that the quadratic equation has no real solutions. Instead, it has two complex solutions. We can proceed to calculate them:
x = (-16 ± √(-144)) / (2 * 2)
Calculating further:
√(-144) = 12i (where i is the imaginary unit)
Now substituting back into the formula gives us:
x = (-16 ± 12i) / 4
This simplifies to:
x = -4 ± 3i
Thus, the solutions are:
x = -4 + 3i and x = -4 – 3i