Answer:
x = -6√3 or 4√3
Step-by-step explanation:
x² + 2√3 x − 72 = 0
Solve with quadratic formula, or completing the square.
To use completing the square, we first add 72 to both sides:
x² + 2√3 x = 72
Take half of 2√3, square it, then add to both sides.
x² + 2√3 + 3 = 75
Factor the perfect square:
(x + √3)² = 75
Solve for x:
x + √3 = ±√75
x + √3 = ±5√3
x = -√3 ± 5√3
x = -6√3 or 4√3
According to Vieta formula, the sum of the roots should equal b/a, and the product of the roots should equal c/a.
-6√3 + 4√3 = 2√3
-6√3 × 4√3 = -72
