x^2+x=0.1156

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Solution for x^2+x=0.1156 equation: 


Simplifying
x2 + x = 0.1156

Reorder the terms:
x + x2 = 0.1156

Solving
x + x2 = 0.1156

Solving for variable 'x'.

Reorder the terms:
-0.1156 + x + x2 = 0.1156 + -0.1156

Combine like terms: 0.1156 + -0.1156 = 0.0000
-0.1156 + x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.1156' to each side of the equation.
-0.1156 + x + 0.1156 + x2 = 0.0000 + 0.1156

Reorder the terms:
-0.1156 + 0.1156 + x + x2 = 0.0000 + 0.1156

Combine like terms: -0.1156 + 0.1156 = 0.0000
0.0000 + x + x2 = 0.0000 + 0.1156
x + x2 = 0.0000 + 0.1156

Combine like terms: 0.0000 + 0.1156 = 0.1156
x + x2 = 0.1156

The x term is x.  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 = 0.1156 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.1156 + 0.25

Combine like terms: 0.1156 + 0.25 = 0.3656
0.25 + x + x2 = 0.3656

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.3656

Calculate the square root of the right side: 0.604648658

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.604648658 and -0.604648658.


Subproblem 1
x + 0.5 = 0.604648658

Simplifying
x + 0.5 = 0.604648658

Reorder the terms:
0.5 + x = 0.604648658

Solving
0.5 + x = 0.604648658

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 = 0.604648658 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.604648658 + -0.5
x = 0.604648658 + -0.5

Combine like terms: 0.604648658 + -0.5 = 0.104648658
x = 0.104648658

Simplifying
x = 0.104648658


Subproblem 2
x + 0.5 = -0.604648658

Simplifying
x + 0.5 = -0.604648658

Reorder the terms:
0.5 + x = -0.604648658

Solving
0.5 + x = -0.604648658

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 = -0.604648658 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.604648658 + -0.5
x = -0.604648658 + -0.5

Combine like terms: -0.604648658 + -0.5 = -1.104648658
x = -1.104648658

Simplifying
x = -1.104648658


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.104648658, -1.104648658}

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