11x^2-6x-2=0

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Solution for 11x^2-6x-2=0 equation: 


Simplifying
11x2 + -6x + -2 = 0

Reorder the terms:
-2 + -6x + 11x2 = 0

Solving
-2 + -6x + 11x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
-0.1818181818 + -0.5454545455x + x2 = 0

Move the constant term to the right:

Add '0.1818181818' to each side of the equation.
-0.1818181818 + -0.5454545455x + 0.1818181818 + x2 = 0 + 0.1818181818

Reorder the terms:
-0.1818181818 + 0.1818181818 + -0.5454545455x + x2 = 0 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + -0.5454545455x + x2 = 0 + 0.1818181818
-0.5454545455x + x2 = 0 + 0.1818181818

Combine like terms: 0 + 0.1818181818 = 0.1818181818
-0.5454545455x + x2 = 0.1818181818

The x term is -0.5454545455x.  Take half its coefficient (-0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
-0.5454545455x + 0.07438016533 + x2 = 0.1818181818 + 0.07438016533

Reorder the terms:
0.07438016533 + -0.5454545455x + x2 = 0.1818181818 + 0.07438016533

Combine like terms: 0.1818181818 + 0.07438016533 = 0.25619834713
0.07438016533 + -0.5454545455x + x2 = 0.25619834713

Factor a perfect square on the left side:
(x + -0.2727272728)(x + -0.2727272728) = 0.25619834713

Calculate the square root of the right side: 0.506160397

Break this problem into two subproblems by setting 
(x + -0.2727272728) equal to 0.506160397 and -0.506160397.


Subproblem 1
x + -0.2727272728 = 0.506160397

Simplifying
x + -0.2727272728 = 0.506160397

Reorder the terms:
-0.2727272728 + x = 0.506160397

Solving
-0.2727272728 + x = 0.506160397

Solving for variable 'x'.

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

Add '0.2727272728' to each side of the equation.
-0.2727272728 + 0.2727272728 + x = 0.506160397 + 0.2727272728

Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000
0.0000000000 + x = 0.506160397 + 0.2727272728
x = 0.506160397 + 0.2727272728

Combine like terms: 0.506160397 + 0.2727272728 = 0.7788876698
x = 0.7788876698

Simplifying
x = 0.7788876698


Subproblem 2
x + -0.2727272728 = -0.506160397

Simplifying
x + -0.2727272728 = -0.506160397

Reorder the terms:
-0.2727272728 + x = -0.506160397

Solving
-0.2727272728 + x = -0.506160397

Solving for variable 'x'.

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

Add '0.2727272728' to each side of the equation.
-0.2727272728 + 0.2727272728 + x = -0.506160397 + 0.2727272728

Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000
0.0000000000 + x = -0.506160397 + 0.2727272728
x = -0.506160397 + 0.2727272728

Combine like terms: -0.506160397 + 0.2727272728 = -0.2334331242
x = -0.2334331242

Simplifying
x = -0.2334331242


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7788876698, -0.2334331242}

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