Final answer:
The equation 2x² + 17x + 44 = -15x - 100 leads to a quadratic in the form of 2x² + 32x + 144 = 0. Using the quadratic formula, we find complex solutions x = -8 + 2√2i and x = -8 - 2√2i, which are not listed in the provided options.
Step-by-step explanation:
To solve the equation 2x² + 17x + 44 = -15x - 100 we first need to move all terms to one side of the equation to get it into standard quadratic form, ax² + bx + c = 0. Combining like terms, we have:
2x² + 17x + 15x + 44 + 100 = 0
2x² + 32x + 144 = 0
Now we use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), where a = 2, b = 32, and c = 144.
The solutions will be:
x = (-32 ± √(32² - 4 × 2 × 144)) / (2 × 2)
x = (-32 ± √(1024 - 1152)) / 4
x = (-32 ± √(-128)) / 4
Since the discriminant (inside the square root) is negative, we will have complex solutions. We can write √(-128) as √(128) × i, where √(128) = 8√2, so:
x = (-32 ± 8√2i) / 4
The final answer will be:
x = -8 ± 2√2i
This means the equation does not have real solutions but it has two complex solutions given by x = -8 + 2√2i and x = -8 - 2√2i which don't match any of the options A through D provided.