6x(x-2)=11

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Solution for 6x(x-2)=11 equation: 


Simplifying
6x(x + -2) = 11

Reorder the terms:
6x(-2 + x) = 11
(-2 * 6x + x * 6x) = 11
(-12x + 6x2) = 11

Solving
-12x + 6x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + -12x + 6x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -12x + 6x2 = 0

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

Divide each side by '6'.
-1.833333333 + -2x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -2x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -2x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.833333333
-2x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-2x + x2 = 1.833333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.833333333 + 1

Reorder the terms:
1 + -2x + x2 = 1.833333333 + 1

Combine like terms: 1.833333333 + 1 = 2.833333333
1 + -2x + x2 = 2.833333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.833333333

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(x + -1) equal to 1.683250823 and -1.683250823.


Subproblem 1
x + -1 = 1.683250823

Simplifying
x + -1 = 1.683250823

Reorder the terms:
-1 + x = 1.683250823

Solving
-1 + x = 1.683250823

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.683250823 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.683250823 + 1
x = 1.683250823 + 1

Combine like terms: 1.683250823 + 1 = 2.683250823
x = 2.683250823

Simplifying
x = 2.683250823


Subproblem 2
x + -1 = -1.683250823

Simplifying
x + -1 = -1.683250823

Reorder the terms:
-1 + x = -1.683250823

Solving
-1 + x = -1.683250823

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.683250823 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.683250823 + 1
x = -1.683250823 + 1

Combine like terms: -1.683250823 + 1 = -0.683250823
x = -0.683250823

Simplifying
x = -0.683250823


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.683250823, -0.683250823}

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