x^2-.6666666667x-2.888888889=0

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Solution for x^2-.6666666667x-2.888888889=0 equation: 


Simplifying
x2 + -0.6666666667x + -2.888888889 = 0

Reorder the terms:
-2.888888889 + -0.6666666667x + x2 = 0

Solving
-2.888888889 + -0.6666666667x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.888888889' to each side of the equation.
-2.888888889 + -0.6666666667x + 2.888888889 + x2 = 0 + 2.888888889

Reorder the terms:
-2.888888889 + 2.888888889 + -0.6666666667x + x2 = 0 + 2.888888889

Combine like terms: -2.888888889 + 2.888888889 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 2.888888889
-0.6666666667x + x2 = 0 + 2.888888889

Combine like terms: 0 + 2.888888889 = 2.888888889
-0.6666666667x + x2 = 2.888888889

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 = 2.888888889 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2.888888889 + 0.1111111112

Combine like terms: 2.888888889 + 0.1111111112 = 3.0000000002
0.1111111112 + -0.6666666667x + x2 = 3.0000000002

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 3.0000000002

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -0.3333333334 = 1.732050808

Simplifying
x + -0.3333333334 = 1.732050808

Reorder the terms:
-0.3333333334 + x = 1.732050808

Solving
-0.3333333334 + x = 1.732050808

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 = 1.732050808 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.732050808 + 0.3333333334
x = 1.732050808 + 0.3333333334

Combine like terms: 1.732050808 + 0.3333333334 = 2.0653841414
x = 2.0653841414

Simplifying
x = 2.0653841414


Subproblem 2
x + -0.3333333334 = -1.732050808

Simplifying
x + -0.3333333334 = -1.732050808

Reorder the terms:
-0.3333333334 + x = -1.732050808

Solving
-0.3333333334 + x = -1.732050808

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 = -1.732050808 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.732050808 + 0.3333333334
x = -1.732050808 + 0.3333333334

Combine like terms: -1.732050808 + 0.3333333334 = -1.3987174746
x = -1.3987174746

Simplifying
x = -1.3987174746


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0653841414, -1.3987174746}

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