x^2-0.6111111111111111x-0.0555555555555556=0

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Solution for x^2-0.6111111111111111x-0.0555555555555556=0 equation: 


Simplifying
x2 + -0.6111111111111111x + -0.0555555555555556 = 0

Reorder the terms:
-0.0555555555555556 + -0.6111111111111111x + x2 = 0

Solving
-0.0555555555555556 + -0.6111111111111111x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0555555555555556' to each side of the equation.
-0.0555555555555556 + -0.6111111111111111x + 0.0555555555555556 + x2 = 0 + 0.0555555555555556

Reorder the terms:
-0.0555555555555556 + 0.0555555555555556 + -0.6111111111111111x + x2 = 0 + 0.0555555555555556

Combine like terms: -0.0555555555555556 + 0.0555555555555556 = 0.0000000000000000
0.0000000000000000 + -0.6111111111111111x + x2 = 0 + 0.0555555555555556
-0.6111111111111111x + x2 = 0 + 0.0555555555555556

Combine like terms: 0 + 0.0555555555555556 = 0.0555555555555556
-0.6111111111111111x + x2 = 0.0555555555555556

The x term is -0.6111111111111111x.  Take half its coefficient (-0.3055555556).
Square it (0.09336419756) and add it to both sides.

Add '0.09336419756' to each side of the equation.
-0.6111111111111111x + 0.09336419756 + x2 = 0.0555555555555556 + 0.09336419756

Reorder the terms:
0.09336419756 + -0.6111111111111111x + x2 = 0.0555555555555556 + 0.09336419756

Combine like terms: 0.0555555555555556 + 0.09336419756 = 0.1489197531155556
0.09336419756 + -0.6111111111111111x + x2 = 0.1489197531155556

Factor a perfect square on the left side:
(x + -0.3055555556)(x + -0.3055555556) = 0.1489197531155556

Calculate the square root of the right side: 0.385901222

Break this problem into two subproblems by setting 
(x + -0.3055555556) equal to 0.385901222 and -0.385901222.


Subproblem 1
x + -0.3055555556 = 0.385901222

Simplifying
x + -0.3055555556 = 0.385901222

Reorder the terms:
-0.3055555556 + x = 0.385901222

Solving
-0.3055555556 + x = 0.385901222

Solving for variable 'x'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + x = 0.385901222 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + x = 0.385901222 + 0.3055555556
x = 0.385901222 + 0.3055555556

Combine like terms: 0.385901222 + 0.3055555556 = 0.6914567776
x = 0.6914567776

Simplifying
x = 0.6914567776


Subproblem 2
x + -0.3055555556 = -0.385901222

Simplifying
x + -0.3055555556 = -0.385901222

Reorder the terms:
-0.3055555556 + x = -0.385901222

Solving
-0.3055555556 + x = -0.385901222

Solving for variable 'x'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + x = -0.385901222 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + x = -0.385901222 + 0.3055555556
x = -0.385901222 + 0.3055555556

Combine like terms: -0.385901222 + 0.3055555556 = -0.0803456664
x = -0.0803456664

Simplifying
x = -0.0803456664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6914567776, -0.0803456664}

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