Quadratic Solver for Casio FX-3650P

[Albert Chan]

Just learn about correction for CCDF function, perhaps useful for above √(2) correction:

Redo above, without solving the quadratic: 0 = y² + 2.828427124 y - 1.055272156e-9 = a y² + b y + c

1st order correction: y ~ t = -c/b
Casio (with internal precision digits), y = 3.73095048851e-10

2nd order correction: y ~ t - (a/b) t²
Casio (with internal precision digits), y = 3.73095048802e-10

√2 ~ 1.414213562 3730950488 02

Edit: Assume a y² + b y + c small real root exist, t = -c/b, w = -(a/b) t = ac/b² :

y = t * (1 + w + 2w^2 + 5w^3 + 14w^4 + 42w^5 + 132w^6 + ...)

Redo above with 40 digits precision: y1 = t, y2 = t + tw ...

y1: 3.730950488509033262969090378444553482510E-10
y2: 3.730950488016887241967143787508642382276E-10
y3: 3.730950488016887242096980785739535431605E-10
y4: 3.730950488016887242096980785696718753754E-10