Solve the equation and check it with the theorem of vieta:

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

or