What are the solutions to the equation 2x² + 16x + 50 = 0?

To find the solutions to the quadratic equation 2x² + 16x + 50 = 0, we can use the quadratic formula, which is given by:

x = (-b ± √(b² – 4ac)) / 2a

In this equation, a, b, and c are the coefficients from the standard form of a quadratic equation ax² + bx + c = 0.

For our equation:

  • a = 2
  • b = 16
  • c = 50

Now, we can plug these values into the quadratic formula:

1. First, we need to calculate the discriminant (b² – 4ac):

b² = 16² = 256

4ac = 4 * 2 * 50 = 400

Discriminant = 256 – 400 = -144

2. Since the discriminant is negative (-144), it indicates that there are no real solutions; instead, there are two complex solutions.

3. Next, we calculate the solutions using the formula:

x = (-16 ± √(-144)) / (2 * 2)

Simplifying this:

x = (-16 ± 12i) / 4

4. We can now simplify further:

x = -4 ± 3i

Thus, the two solutions to the equation 2x² + 16x + 50 = 0 are:

  • x = -4 + 3i
  • x = -4 – 3i

In conclusion, the equation has two complex solutions: -4 + 3i and -4 – 3i. These solutions reflect the nature of quadratic equations where the discriminant is negative, indicating the curve does not intersect the x-axis.

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