Partial Solutions For Extended Einsteinian Formulas:

Since,

        mc^2                       mc^2
E = -------------    and    E = --------, then,
             v^2                    mc^2
    sqrt(1 - ---)               1 + ----
             c^2                     Ep

cross multiply,

         mc^2                  v^2
mc^2(1 + ----) = mc^2(sqrt(1 - ---)), then,
          Ep                   c^2

    mc^2              v^2          mc^2            v^2
1 + ----  =  sqrt(1 - ---),   (1 + ----)^2  =  1 - ---,
     Ep               c^2           Ep             c^2

        mc^2   m^2 * c^4         v^2
1 + 2 * ---- + ---------  =  1 - ---,
         Ep       Ep^2           c^2


2 * mc^2   m^2 * c^4       v^2
-------- + ---------  =  - ---,
   Ep         Ep^2         c^2


Ep * 2 * mc^2   m^2 * c^4       v^2
------------- + ---------  =  - ---,
    Ep^2          Ep^2          c^2


Ep * 2 * mc^2 + m^2 * c^4       v^2
-------------------------  =  - ---,
    Ep^2                        c^2


mc^2(Ep * 2 + mc^2)       v^2
-------------------  =  - ---,
    Ep^2                  c^2

cross multiply:

mc^4(Ep * 2 + mc^2) = -v^2 * Ep^2, then,

2 * Ep * mc^4 + m^2 * c^6 = -v^2 * Ep^2,

2 * Ep * mc^4 + m^2 * c^6 + v^2 * Ep^2 = 0,

Ep^2 * v^2 + Ep * 2 * mc^4 + m^2 * c^6 = 0,

                                     -b + sqrt(b ^ 2 - 4 * a * c)
If a * x^2 + b * x + c = 0, and  x = ----------------------------
                                               2 * a

and, a = v^2, b = 2 * mc^4, c = m^2 * c^6, x = Ep, then,

      -mc^4 + sqrt((2 * mc^4)^2 - 4 * v^2 * m^2 * c^6)
Ep =  -----------------------------------------------,
                        v^2

because, a^2 - b^2 = (a + b) * (a - b), then, Ep = 

(equation #1):

-mc^4 + sqrt((2 * mc^4 + 2 * v * mc^3) * (2 * mc^4 - 2 * v * mc^3))
-------------------------------------------------------------------,
                  v^2

then in a partial solution for the term: 2 * mc^4 + 2 * v * mc^3,

E = 2 * mc^4 + 2 * v * mc^3, E - 2 * mc^4 = 2 * v * mc^3,

E - 2 * mc^4 = mc^3,
------------
    2 * v

  E     2 * mc^4
----- - -------- = mc^3, finally,
2 * v    2 * v

  1
----- * E + C = mc^3, therefore,
2 * v

nE + C = mc^3.