s^2=1+s(1-6s)

Solution for s^2=1+s(1-6s) equation:

Simplifying
s2 = 1 + s(1 + -6s)
s2 = 1 + (1 * s + -6s * s)
s2 = 1 + (1s + -6s2)

Solving
s2 = 1 + 1s + -6s2

Solving for variable 's'.

Reorder the terms:
-1 + -1s + s2 + 6s2 = 1 + 1s + -6s2 + -1 + -1s + 6s2

Combine like terms: s2 + 6s2 = 7s2
-1 + -1s + 7s2 = 1 + 1s + -6s2 + -1 + -1s + 6s2

Reorder the terms:
-1 + -1s + 7s2 = 1 + -1 + 1s + -1s + -6s2 + 6s2

Combine like terms: 1 + -1 = 0
-1 + -1s + 7s2 = 0 + 1s + -1s + -6s2 + 6s2
-1 + -1s + 7s2 = 1s + -1s + -6s2 + 6s2

Combine like terms: 1s + -1s = 0
-1 + -1s + 7s2 = 0 + -6s2 + 6s2
-1 + -1s + 7s2 = -6s2 + 6s2

Combine like terms: -6s2 + 6s2 = 0
-1 + -1s + 7s2 = 0

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

Divide each side by '7'.
-0.1428571429 + -0.1428571429s + s2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -0.1428571429s + 0.1428571429 + s2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -0.1428571429s + s2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -0.1428571429s + s2 = 0 + 0.1428571429
-0.1428571429s + s2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-0.1428571429s + s2 = 0.1428571429

The s term is -0.1428571429s.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429s + 0.005102040819 + s2 = 0.1428571429 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429s + s2 = 0.1428571429 + 0.005102040819

Combine like terms: 0.1428571429 + 0.005102040819 = 0.147959183719
0.005102040819 + -0.1428571429s + s2 = 0.147959183719

Factor a perfect square on the left side:
(s + -0.07142857145)(s + -0.07142857145) = 0.147959183719

Calculate the square root of the right side: 0.384654629

Break this problem into two subproblems by setting 
(s + -0.07142857145) equal to 0.384654629 and -0.384654629.

Subproblem 1
s + -0.07142857145 = 0.384654629

Simplifying
s + -0.07142857145 = 0.384654629

Reorder the terms:
-0.07142857145 + s = 0.384654629

Solving
-0.07142857145 + s = 0.384654629

Solving for variable 's'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + s = 0.384654629 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + s = 0.384654629 + 0.07142857145
s = 0.384654629 + 0.07142857145

Combine like terms: 0.384654629 + 0.07142857145 = 0.45608320045
s = 0.45608320045

Simplifying
s = 0.45608320045

Subproblem 2
s + -0.07142857145 = -0.384654629

Simplifying
s + -0.07142857145 = -0.384654629

Reorder the terms:
-0.07142857145 + s = -0.384654629

Solving
-0.07142857145 + s = -0.384654629

Solving for variable 's'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + s = -0.384654629 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + s = -0.384654629 + 0.07142857145
s = -0.384654629 + 0.07142857145

Combine like terms: -0.384654629 + 0.07142857145 = -0.31322605755
s = -0.31322605755

Simplifying
s = -0.31322605755

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.45608320045, -0.31322605755}