0.1111111112-0.6666666667x+x^2=3.1111111112

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Solution for 0.1111111112-0.6666666667x+x^2=3.1111111112 equation: 


Simplifying
0.1111111112 + -0.6666666667x + x2 = 3.1111111112

Solving
0.1111111112 + -0.6666666667x + x2 = 3.1111111112

Solving for variable 'x'.

Reorder the terms:
0.1111111112 + -3.1111111112 + -0.6666666667x + x2 = 3.1111111112 + -3.1111111112

Combine like terms: 0.1111111112 + -3.1111111112 = -3
-3 + -0.6666666667x + x2 = 3.1111111112 + -3.1111111112

Combine like terms: 3.1111111112 + -3.1111111112 = 0.0000000000
-3 + -0.6666666667x + x2 = 0.0000000000

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.6666666667x + 3 + x2 = 0.0000000000 + 3

Reorder the terms:
-3 + 3 + -0.6666666667x + x2 = 0.0000000000 + 3

Combine like terms: -3 + 3 = 0
0 + -0.6666666667x + x2 = 0.0000000000 + 3
-0.6666666667x + x2 = 0.0000000000 + 3

Combine like terms: 0.0000000000 + 3 = 3
-0.6666666667x + x2 = 3

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 3 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 3 + 0.1111111112

Combine like terms: 3 + 0.1111111112 = 3.1111111112
0.1111111112 + -0.6666666667x + x2 = 3.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 3.1111111112

Calculate the square root of the right side: 1.763834207

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.763834207 and -1.763834207.


Subproblem 1
x + -0.3333333334 = 1.763834207

Simplifying
x + -0.3333333334 = 1.763834207

Reorder the terms:
-0.3333333334 + x = 1.763834207

Solving
-0.3333333334 + x = 1.763834207

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.763834207 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.763834207 + 0.3333333334
x = 1.763834207 + 0.3333333334

Combine like terms: 1.763834207 + 0.3333333334 = 2.0971675404
x = 2.0971675404

Simplifying
x = 2.0971675404


Subproblem 2
x + -0.3333333334 = -1.763834207

Simplifying
x + -0.3333333334 = -1.763834207

Reorder the terms:
-0.3333333334 + x = -1.763834207

Solving
-0.3333333334 + x = -1.763834207

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.763834207 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.763834207 + 0.3333333334
x = -1.763834207 + 0.3333333334

Combine like terms: -1.763834207 + 0.3333333334 = -1.4305008736
x = -1.4305008736

Simplifying
x = -1.4305008736


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0971675404, -1.4305008736}

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