4s+4s^2=1

Solution for 4s+4s^2=1 equation:

Simplifying
4s + 4s2 = 1

Solving
4s + 4s2 = 1

Solving for variable 's'.

Reorder the terms:
-1 + 4s + 4s2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4s + 4s2 = 0

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

Divide each side by '4'.
-0.25 + s + s2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + s + 0.25 + s2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + s + s2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + s + s2 = 0 + 0.25
s + s2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
s + s2 = 0.25

The s term is s.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + s2 = 0.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + s2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
1.25 + s2 = 0.5

Factor a perfect square on the left side:
(s + 0.5)(s + 0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(s + 0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
s + 0.5 = 0.707106781

Simplifying
s + 0.5 = 0.707106781

Reorder the terms:
0.5 + s = 0.707106781

Solving
0.5 + s = 0.707106781

Solving for variable 's'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + s = 0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + s = 0.707106781 + -0.5
s = 0.707106781 + -0.5

Combine like terms: 0.707106781 + -0.5 = 0.207106781
s = 0.207106781

Simplifying
s = 0.207106781

Subproblem 2
s + 0.5 = -0.707106781

Simplifying
s + 0.5 = -0.707106781

Reorder the terms:
0.5 + s = -0.707106781

Solving
0.5 + s = -0.707106781

Solving for variable 's'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + s = -0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + s = -0.707106781 + -0.5
s = -0.707106781 + -0.5

Combine like terms: -0.707106781 + -0.5 = -1.207106781
s = -1.207106781

Simplifying
s = -1.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.207106781, -1.207106781}