Answer:
Therefore, the answer is D. 3+√-3, -6.
Explanation:
First, we can simplify the equation by subtracting 5x² and 9x from both sides:
2x² + 6x + 2 - 5x² - 9x - 3 = 0
Simplifying further:
-3x² - 3x - 1 = 0
Now we can apply the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -3, b = -3, and c = -1.
Plugging in these values, we get:
x = (-(-3) ± sqrt((-3)^2 - 4(-3)(-1))) / 2(-3)
x = (3 ± sqrt(9 - 12)) / (-6)
x = (3 ± sqrt(-3)) / (-6)
Since the square root of -3 is an imaginary number, the solutions are complex conjugates:
x = (3 + sqrt(-3)) / (-6) or x = (3 - sqrt(-3)) / (-6)
Simplifying further:
x = (-1/2) - (sqrt(3) i) / 6 or x = (-1/2) + (sqrt(3) i) / 6
Therefore, the answer is D. 3+√-3, -6.