6x^2+7x-11=0

Solution for 6x^2+7x-11=0 equation:

Simplifying
6x2 + 7x + -11 = 0

Reorder the terms:
-11 + 7x + 6x2 = 0

Solving
-11 + 7x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-1.833333333 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 1.166666667x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 1.166666667x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 1.166666667x + x2 = 0 + 1.833333333
1.166666667x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
1.166666667x + x2 = 1.833333333

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = 1.833333333 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = 1.833333333 + 0.3402777780

Combine like terms: 1.833333333 + 0.3402777780 = 2.173611111
0.3402777780 + 1.166666667x + x2 = 2.173611111

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 2.173611111

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 1.474317168 and -1.474317168.

Subproblem 1
x + 0.5833333335 = 1.474317168

Simplifying
x + 0.5833333335 = 1.474317168

Reorder the terms:
0.5833333335 + x = 1.474317168

Solving
0.5833333335 + x = 1.474317168

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = 1.474317168 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = 1.474317168 + -0.5833333335
x = 1.474317168 + -0.5833333335

Combine like terms: 1.474317168 + -0.5833333335 = 0.8909838345
x = 0.8909838345

Simplifying
x = 0.8909838345

Subproblem 2
x + 0.5833333335 = -1.474317168

Simplifying
x + 0.5833333335 = -1.474317168

Reorder the terms:
0.5833333335 + x = -1.474317168

Solving
0.5833333335 + x = -1.474317168

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = -1.474317168 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = -1.474317168 + -0.5833333335
x = -1.474317168 + -0.5833333335

Combine like terms: -1.474317168 + -0.5833333335 = -2.0576505015
x = -2.0576505015

Simplifying
x = -2.0576505015

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8909838345, -2.0576505015}