s^2+s=0.66

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Solution for s^2+s=0.66 equation:


Simplifying
s2 + s = 0.66

Reorder the terms:
s + s2 = 0.66

Solving
s + s2 = 0.66

Solving for variable 's'.

Reorder the terms:
-0.66 + s + s2 = 0.66 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
-0.66 + s + s2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.66' to each side of the equation.
-0.66 + s + 0.66 + s2 = 0.00 + 0.66

Reorder the terms:
-0.66 + 0.66 + s + s2 = 0.00 + 0.66

Combine like terms: -0.66 + 0.66 = 0.00
0.00 + s + s2 = 0.00 + 0.66
s + s2 = 0.00 + 0.66

Combine like terms: 0.00 + 0.66 = 0.66
s + s2 = 0.66

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.
s + 0.25 + s2 = 0.66 + 0.25

Reorder the terms:
0.25 + s + s2 = 0.66 + 0.25

Combine like terms: 0.66 + 0.25 = 0.91
0.25 + s + s2 = 0.91

Factor a perfect square on the left side:
(s + 0.5)(s + 0.5) = 0.91

Calculate the square root of the right side: 0.953939201

Break this problem into two subproblems by setting 
(s + 0.5) equal to 0.953939201 and -0.953939201.


Subproblem 1
s + 0.5 = 0.953939201

Simplifying
s + 0.5 = 0.953939201

Reorder the terms:
0.5 + s = 0.953939201

Solving
0.5 + s = 0.953939201

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 = 0.953939201 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + s = 0.953939201 + -0.5
s = 0.953939201 + -0.5

Combine like terms: 0.953939201 + -0.5 = 0.453939201
s = 0.453939201

Simplifying
s = 0.453939201


Subproblem 2
s + 0.5 = -0.953939201

Simplifying
s + 0.5 = -0.953939201

Reorder the terms:
0.5 + s = -0.953939201

Solving
0.5 + s = -0.953939201

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 = -0.953939201 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + s = -0.953939201 + -0.5
s = -0.953939201 + -0.5

Combine like terms: -0.953939201 + -0.5 = -1.453939201
s = -1.453939201

Simplifying
s = -1.453939201


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.453939201, -1.453939201}

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