x^2-0.66667x-2.88889=0

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Solution for x^2-0.66667x-2.88889=0 equation: 


Simplifying
x2 + -0.66667x + -2.88889 = 0

Reorder the terms:
-2.88889 + -0.66667x + x2 = 0

Solving
-2.88889 + -0.66667x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.88889' to each side of the equation.
-2.88889 + -0.66667x + 2.88889 + x2 = 0 + 2.88889

Reorder the terms:
-2.88889 + 2.88889 + -0.66667x + x2 = 0 + 2.88889

Combine like terms: -2.88889 + 2.88889 = 0.00000
0.00000 + -0.66667x + x2 = 0 + 2.88889
-0.66667x + x2 = 0 + 2.88889

Combine like terms: 0 + 2.88889 = 2.88889
-0.66667x + x2 = 2.88889

The x term is -0.66667x.  Take half its coefficient (-0.333335).
Square it (0.1111122222) and add it to both sides.

Add '0.1111122222' to each side of the equation.
-0.66667x + 0.1111122222 + x2 = 2.88889 + 0.1111122222

Reorder the terms:
0.1111122222 + -0.66667x + x2 = 2.88889 + 0.1111122222

Combine like terms: 2.88889 + 0.1111122222 = 3.0000022222
0.1111122222 + -0.66667x + x2 = 3.0000022222

Factor a perfect square on the left side:
(x + -0.333335)(x + -0.333335) = 3.0000022222

Calculate the square root of the right side: 1.732051449

Break this problem into two subproblems by setting 
(x + -0.333335) equal to 1.732051449 and -1.732051449.


Subproblem 1
x + -0.333335 = 1.732051449

Simplifying
x + -0.333335 = 1.732051449

Reorder the terms:
-0.333335 + x = 1.732051449

Solving
-0.333335 + x = 1.732051449

Solving for variable 'x'.

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

Add '0.333335' to each side of the equation.
-0.333335 + 0.333335 + x = 1.732051449 + 0.333335

Combine like terms: -0.333335 + 0.333335 = 0.000000
0.000000 + x = 1.732051449 + 0.333335
x = 1.732051449 + 0.333335

Combine like terms: 1.732051449 + 0.333335 = 2.065386449
x = 2.065386449

Simplifying
x = 2.065386449


Subproblem 2
x + -0.333335 = -1.732051449

Simplifying
x + -0.333335 = -1.732051449

Reorder the terms:
-0.333335 + x = -1.732051449

Solving
-0.333335 + x = -1.732051449

Solving for variable 'x'.

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

Add '0.333335' to each side of the equation.
-0.333335 + 0.333335 + x = -1.732051449 + 0.333335

Combine like terms: -0.333335 + 0.333335 = 0.000000
0.000000 + x = -1.732051449 + 0.333335
x = -1.732051449 + 0.333335

Combine like terms: -1.732051449 + 0.333335 = -1.398716449
x = -1.398716449

Simplifying
x = -1.398716449


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.065386449, -1.398716449}

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