x^2+x=3.1156

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Solution for x^2+x=3.1156 equation: 


Simplifying
x2 + x = 3.1156

Reorder the terms:
x + x2 = 3.1156

Solving
x + x2 = 3.1156

Solving for variable 'x'.

Reorder the terms:
-3.1156 + x + x2 = 3.1156 + -3.1156

Combine like terms: 3.1156 + -3.1156 = 0.0000
-3.1156 + x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '3.1156' to each side of the equation.
-3.1156 + x + 3.1156 + x2 = 0.0000 + 3.1156

Reorder the terms:
-3.1156 + 3.1156 + x + x2 = 0.0000 + 3.1156

Combine like terms: -3.1156 + 3.1156 = 0.0000
0.0000 + x + x2 = 0.0000 + 3.1156
x + x2 = 0.0000 + 3.1156

Combine like terms: 0.0000 + 3.1156 = 3.1156
x + x2 = 3.1156

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 = 3.1156 + 0.25

Reorder the terms:
0.25 + x + x2 = 3.1156 + 0.25

Combine like terms: 3.1156 + 0.25 = 3.3656
0.25 + x + x2 = 3.3656

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.3656

Calculate the square root of the right side: 1.834557167

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.834557167 and -1.834557167.


Subproblem 1
x + 0.5 = 1.834557167

Simplifying
x + 0.5 = 1.834557167

Reorder the terms:
0.5 + x = 1.834557167

Solving
0.5 + x = 1.834557167

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 = 1.834557167 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.834557167 + -0.5
x = 1.834557167 + -0.5

Combine like terms: 1.834557167 + -0.5 = 1.334557167
x = 1.334557167

Simplifying
x = 1.334557167


Subproblem 2
x + 0.5 = -1.834557167

Simplifying
x + 0.5 = -1.834557167

Reorder the terms:
0.5 + x = -1.834557167

Solving
0.5 + x = -1.834557167

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 = -1.834557167 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.834557167 + -0.5
x = -1.834557167 + -0.5

Combine like terms: -1.834557167 + -0.5 = -2.334557167
x = -2.334557167

Simplifying
x = -2.334557167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.334557167, -2.334557167}

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