x^2+x=.1109

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Solution for x^2+x=.1109 equation: 


Simplifying
x2 + x = 0.1109

Reorder the terms:
x + x2 = 0.1109

Solving
x + x2 = 0.1109

Solving for variable 'x'.

Reorder the terms:
-0.1109 + x + x2 = 0.1109 + -0.1109

Combine like terms: 0.1109 + -0.1109 = 0.0000
-0.1109 + x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.1109' to each side of the equation.
-0.1109 + x + 0.1109 + x2 = 0.0000 + 0.1109

Reorder the terms:
-0.1109 + 0.1109 + x + x2 = 0.0000 + 0.1109

Combine like terms: -0.1109 + 0.1109 = 0.0000
0.0000 + x + x2 = 0.0000 + 0.1109
x + x2 = 0.0000 + 0.1109

Combine like terms: 0.0000 + 0.1109 = 0.1109
x + x2 = 0.1109

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 = 0.1109 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.1109 + 0.25

Combine like terms: 0.1109 + 0.25 = 0.3609
0.25 + x + x2 = 0.3609

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.3609

Calculate the square root of the right side: 0.600749532

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.600749532 and -0.600749532.


Subproblem 1
x + 0.5 = 0.600749532

Simplifying
x + 0.5 = 0.600749532

Reorder the terms:
0.5 + x = 0.600749532

Solving
0.5 + x = 0.600749532

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 = 0.600749532 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.600749532 + -0.5
x = 0.600749532 + -0.5

Combine like terms: 0.600749532 + -0.5 = 0.100749532
x = 0.100749532

Simplifying
x = 0.100749532


Subproblem 2
x + 0.5 = -0.600749532

Simplifying
x + 0.5 = -0.600749532

Reorder the terms:
0.5 + x = -0.600749532

Solving
0.5 + x = -0.600749532

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 = -0.600749532 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.600749532 + -0.5
x = -0.600749532 + -0.5

Combine like terms: -0.600749532 + -0.5 = -1.100749532
x = -1.100749532

Simplifying
x = -1.100749532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.100749532, -1.100749532}

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