458984k+1=35785(k+56)*5789k

Solution for 458984k+1=35785(k+56)*5789k equation:

Simplifying
458984k + 1 = 35785(k + 56) * 5789k

Reorder the terms:
1 + 458984k = 35785(k + 56) * 5789k

Reorder the terms:
1 + 458984k = 35785(56 + k) * 5789k

Reorder the terms for easier multiplication:
1 + 458984k = 35785 * 5789k(56 + k)

Multiply 35785 * 5789
1 + 458984k = 207159365k(56 + k)
1 + 458984k = (56 * 207159365k + k * 207159365k)
1 + 458984k = (11600924440k + 207159365k2)

Solving
1 + 458984k = 11600924440k + 207159365k2

Solving for variable 'k'.

Combine like terms: 458984k + -11600924440k = -11600465456k
1 + -11600465456k + -207159365k2 = 11600924440k + 207159365k2 + -11600924440k + -207159365k2

Reorder the terms:
1 + -11600465456k + -207159365k2 = 11600924440k + -11600924440k + 207159365k2 + -207159365k2

Combine like terms: 11600924440k + -11600924440k = 0
1 + -11600465456k + -207159365k2 = 0 + 207159365k2 + -207159365k2
1 + -11600465456k + -207159365k2 = 207159365k2 + -207159365k2

Combine like terms: 207159365k2 + -207159365k2 = 0
1 + -11600465456k + -207159365k2 = 0

Begin completing the square.  Divide all terms by
-207159365 the coefficient of the squared term: 

Divide each side by '-207159365'.
-0.000000004827201512 + 55.99778439k + k2 = 0

Move the constant term to the right:

Add '0.000000004827201512' to each side of the equation.
-0.000000004827201512 + 55.99778439k + 0.000000004827201512 + k2 = 0 + 0.000000004827201512

Reorder the terms:
-0.000000004827201512 + 0.000000004827201512 + 55.99778439k + k2 = 0 + 0.000000004827201512

Combine like terms: -0.000000004827201512 + 0.000000004827201512 = 0.000000000000000000
0.000000000000000000 + 55.99778439k + k2 = 0 + 0.000000004827201512
55.99778439k + k2 = 0 + 0.000000004827201512

Combine like terms: 0 + 0.000000004827201512 = 0.000000004827201512
55.99778439k + k2 = 0.000000004827201512

The k term is 55.99778439k.  Take half its coefficient (27.9988922).
Square it (783.9379644) and add it to both sides.

Add '783.9379644' to each side of the equation.
55.99778439k + 783.9379644 + k2 = 0.000000004827201512 + 783.9379644

Reorder the terms:
783.9379644 + 55.99778439k + k2 = 0.000000004827201512 + 783.9379644

Combine like terms: 0.000000004827201512 + 783.9379644 = 783.937964404827201512
783.9379644 + 55.99778439k + k2 = 783.937964404827201512

Factor a perfect square on the left side:
(k + 27.9988922)(k + 27.9988922) = 783.937964404827201512

Calculate the square root of the right side: 27.9988922

Break this problem into two subproblems by setting 
(k + 27.9988922) equal to 27.9988922 and -27.9988922.

Subproblem 1
k + 27.9988922 = 27.9988922

Simplifying
k + 27.9988922 = 27.9988922

Reorder the terms:
27.9988922 + k = 27.9988922

Add '-27.9988922' to each side of the equation.
27.9988922 + -27.9988922 + k = 27.9988922 + -27.9988922

Combine like terms: 27.9988922 + -27.9988922 = 0.0000000
0.0000000 + k = 27.9988922 + -27.9988922
k = 27.9988922 + -27.9988922

Combine like terms: 27.9988922 + -27.9988922 = 0.0000000
k = 0.0000000

Solving
k = 0.0000000

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Simplifying
k = 0.0000000

Subproblem 2
k + 27.9988922 = -27.9988922

Simplifying
k + 27.9988922 = -27.9988922

Reorder the terms:
27.9988922 + k = -27.9988922

Solving
27.9988922 + k = -27.9988922

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-27.9988922' to each side of the equation.
27.9988922 + -27.9988922 + k = -27.9988922 + -27.9988922

Combine like terms: 27.9988922 + -27.9988922 = 0.0000000
0.0000000 + k = -27.9988922 + -27.9988922
k = -27.9988922 + -27.9988922

Combine like terms: -27.9988922 + -27.9988922 = -55.9977844
k = -55.9977844

Simplifying
k = -55.9977844

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.0000000, -55.9977844}