x(1+x)=0.116

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Solution for x(1+x)=0.116 equation: 


Simplifying
x(1 + x) = 0.116
(1 * x + x * x) = 0.116
(1x + x2) = 0.116

Solving
1x + x2 = 0.116

Solving for variable 'x'.

Reorder the terms:
-0.116 + 1x + x2 = 0.116 + -0.116

Combine like terms: 0.116 + -0.116 = 0.000
-0.116 + 1x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.116' to each side of the equation.
-0.116 + 1x + 0.116 + x2 = 0.000 + 0.116

Reorder the terms:
-0.116 + 0.116 + 1x + x2 = 0.000 + 0.116

Combine like terms: -0.116 + 0.116 = 0.000
0.000 + 1x + x2 = 0.000 + 0.116
1x + x2 = 0.000 + 0.116

Combine like terms: 0.000 + 0.116 = 0.116
1x + x2 = 0.116

The x term is 1x.  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.
x + 0.25 + x2 = 0.116 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.116 + 0.25

Combine like terms: 0.116 + 0.25 = 0.366
0.25 + x + x2 = 0.366

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.366

Calculate the square root of the right side: 0.604979338

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.604979338 and -0.604979338.


Subproblem 1
x + 0.5 = 0.604979338

Simplifying
x + 0.5 = 0.604979338

Reorder the terms:
0.5 + x = 0.604979338

Solving
0.5 + x = 0.604979338

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.604979338 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.604979338 + -0.5
x = 0.604979338 + -0.5

Combine like terms: 0.604979338 + -0.5 = 0.104979338
x = 0.104979338

Simplifying
x = 0.104979338


Subproblem 2
x + 0.5 = -0.604979338

Simplifying
x + 0.5 = -0.604979338

Reorder the terms:
0.5 + x = -0.604979338

Solving
0.5 + x = -0.604979338

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.604979338 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.604979338 + -0.5
x = -0.604979338 + -0.5

Combine like terms: -0.604979338 + -0.5 = -1.104979338
x = -1.104979338

Simplifying
x = -1.104979338


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.104979338, -1.104979338}

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