Final answer:
To solve the quadratic equation -√3x² - 2√2x - 2√3 = 0, use the quadratic formula with a = -√3, b = -2√2, and c = -2√3. Simplify the formula to get x = -(√2 ± 2√2)√3 / 3.
Step-by-step explanation:
To solve the quadratic equation -√3x² - 2√2x - 2√3 = 0, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the quadratic formula states that x = (-b ± √(b² - 4ac)) / (2a).
In this case, a = -√3, b = -2√2, and c = -2√3. Substituting these values into the quadratic formula, we get:
x = (-(-2√2) ± √((-2√2)² - 4(-√3)(-2√3))) / (2(-√3))
Simplifying further, we have:
x = (2√2 ± √(8 + 24)) / (-2√3)
x = (2√2 ± √32) / (-2√3)
x = (√2 ± 2√2) / (-√3)
x = -(√2 ± 2√2)√3 / 3