=3x^2-11x-6

Solution for =3x^2-11x-6 equation:

Simplifying
0 = 3x2 + -11x + -6

Reorder the terms:
0 = -6 + -11x + 3x2

Solving
0 = -6 + -11x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 11x + -3x2 = -6 + -11x + 3x2 + 6 + 11x + -3x2

Reorder the terms:
6 + 11x + -3x2 = -6 + 6 + -11x + 11x + 3x2 + -3x2

Combine like terms: -6 + 6 = 0
6 + 11x + -3x2 = 0 + -11x + 11x + 3x2 + -3x2
6 + 11x + -3x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
6 + 11x + -3x2 = 0 + 3x2 + -3x2
6 + 11x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + 11x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.666666667x + x2 = 0 + 2
-3.666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.666666667x + x2 = 2

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 2 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 2 + 3.361111114

Combine like terms: 2 + 3.361111114 = 5.361111114
3.361111114 + -3.666666667x + x2 = 5.361111114

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 5.361111114

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 2.315407332 and -2.315407332.

Subproblem 1
x + -1.833333334 = 2.315407332

Simplifying
x + -1.833333334 = 2.315407332

Reorder the terms:
-1.833333334 + x = 2.315407332

Solving
-1.833333334 + x = 2.315407332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 2.315407332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 2.315407332 + 1.833333334
x = 2.315407332 + 1.833333334

Combine like terms: 2.315407332 + 1.833333334 = 4.148740666
x = 4.148740666

Simplifying
x = 4.148740666

Subproblem 2
x + -1.833333334 = -2.315407332

Simplifying
x + -1.833333334 = -2.315407332

Reorder the terms:
-1.833333334 + x = -2.315407332

Solving
-1.833333334 + x = -2.315407332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -2.315407332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -2.315407332 + 1.833333334
x = -2.315407332 + 1.833333334

Combine like terms: -2.315407332 + 1.833333334 = -0.482073998
x = -0.482073998

Simplifying
x = -0.482073998

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.148740666, -0.482073998}