We are to solve using completing the square:
1/4x² + x + 1/4 = 0
Let's collect like terms:
1/4x² + x = -1/4
Divide both sides by the coefficient of x-squared:
x² + 4x = -1
Take half of the coefficient of x, square it, then add to both sides:
x² + 4x + 4 = -1 + 4
factor the left side of the equation:
(x + 2)² = 3
Take the root of both sides;
x + 2 = ±√3
Add 2 to both sides:
x = ±√(3) - 2
x = -2 + √3 or x = -2 - √3
herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3