x+x^2=2.2093

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Solution for x+x^2=2.2093 equation: 


Simplifying
x + x2 = 2.2093

Solving
x + x2 = 2.2093

Solving for variable 'x'.

Reorder the terms:
-2.2093 + x + x2 = 2.2093 + -2.2093

Combine like terms: 2.2093 + -2.2093 = 0.0000
-2.2093 + x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '2.2093' to each side of the equation.
-2.2093 + x + 2.2093 + x2 = 0.0000 + 2.2093

Reorder the terms:
-2.2093 + 2.2093 + x + x2 = 0.0000 + 2.2093

Combine like terms: -2.2093 + 2.2093 = 0.0000
0.0000 + x + x2 = 0.0000 + 2.2093
x + x2 = 0.0000 + 2.2093

Combine like terms: 0.0000 + 2.2093 = 2.2093
x + x2 = 2.2093

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 = 2.2093 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.2093 + 0.25

Combine like terms: 2.2093 + 0.25 = 2.4593
0.25 + x + x2 = 2.4593

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.4593

Calculate the square root of the right side: 1.568215546

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.568215546 and -1.568215546.


Subproblem 1
x + 0.5 = 1.568215546

Simplifying
x + 0.5 = 1.568215546

Reorder the terms:
0.5 + x = 1.568215546

Solving
0.5 + x = 1.568215546

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 = 1.568215546 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.568215546 + -0.5
x = 1.568215546 + -0.5

Combine like terms: 1.568215546 + -0.5 = 1.068215546
x = 1.068215546

Simplifying
x = 1.068215546


Subproblem 2
x + 0.5 = -1.568215546

Simplifying
x + 0.5 = -1.568215546

Reorder the terms:
0.5 + x = -1.568215546

Solving
0.5 + x = -1.568215546

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 = -1.568215546 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.568215546 + -0.5
x = -1.568215546 + -0.5

Combine like terms: -1.568215546 + -0.5 = -2.068215546
x = -2.068215546

Simplifying
x = -2.068215546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.068215546, -2.068215546}

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