s^2=6+s(1-9s)

Solution for s^2=6+s(1-9s) equation:

Simplifying
s2 = 6 + s(1 + -9s)
s2 = 6 + (1 * s + -9s * s)
s2 = 6 + (1s + -9s2)

Solving
s2 = 6 + 1s + -9s2

Solving for variable 's'.

Reorder the terms:
-6 + -1s + s2 + 9s2 = 6 + 1s + -9s2 + -6 + -1s + 9s2

Combine like terms: s2 + 9s2 = 10s2
-6 + -1s + 10s2 = 6 + 1s + -9s2 + -6 + -1s + 9s2

Reorder the terms:
-6 + -1s + 10s2 = 6 + -6 + 1s + -1s + -9s2 + 9s2

Combine like terms: 6 + -6 = 0
-6 + -1s + 10s2 = 0 + 1s + -1s + -9s2 + 9s2
-6 + -1s + 10s2 = 1s + -1s + -9s2 + 9s2

Combine like terms: 1s + -1s = 0
-6 + -1s + 10s2 = 0 + -9s2 + 9s2
-6 + -1s + 10s2 = -9s2 + 9s2

Combine like terms: -9s2 + 9s2 = 0
-6 + -1s + 10s2 = 0

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

Divide each side by '10'.
-0.6 + -0.1s + s2 = 0.0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.1s + 0.6 + s2 = 0.0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.1s + s2 = 0.0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.1s + s2 = 0.0 + 0.6
-0.1s + s2 = 0.0 + 0.6

Combine like terms: 0.0 + 0.6 = 0.6
-0.1s + s2 = 0.6

The s term is -0.1s.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1s + 0.0025 + s2 = 0.6 + 0.0025

Reorder the terms:
0.0025 + -0.1s + s2 = 0.6 + 0.0025

Combine like terms: 0.6 + 0.0025 = 0.6025
0.0025 + -0.1s + s2 = 0.6025

Factor a perfect square on the left side:
(s + -0.05)(s + -0.05) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(s + -0.05) equal to 0.776208735 and -0.776208735.

Subproblem 1
s + -0.05 = 0.776208735

Simplifying
s + -0.05 = 0.776208735

Reorder the terms:
-0.05 + s = 0.776208735

Solving
-0.05 + s = 0.776208735

Solving for variable 's'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + s = 0.776208735 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + s = 0.776208735 + 0.05
s = 0.776208735 + 0.05

Combine like terms: 0.776208735 + 0.05 = 0.826208735
s = 0.826208735

Simplifying
s = 0.826208735

Subproblem 2
s + -0.05 = -0.776208735

Simplifying
s + -0.05 = -0.776208735

Reorder the terms:
-0.05 + s = -0.776208735

Solving
-0.05 + s = -0.776208735

Solving for variable 's'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + s = -0.776208735 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + s = -0.776208735 + 0.05
s = -0.776208735 + 0.05

Combine like terms: -0.776208735 + 0.05 = -0.726208735
s = -0.726208735

Simplifying
s = -0.726208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.826208735, -0.726208735}