12x^2-11x-12=

Solution for 12x^2-11x-12= equation:

Simplifying
12x2 + -11x + -12 = 0

Reorder the terms:
-12 + -11x + 12x2 = 0

Solving
-12 + -11x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-1 + -0.9166666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.9166666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.9166666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.9166666667x + x2 = 0 + 1
-0.9166666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.9166666667x + x2 = 1

The x term is -0.9166666667x.  Take half its coefficient (-0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
-0.9166666667x + 0.2100694445 + x2 = 1 + 0.2100694445

Reorder the terms:
0.2100694445 + -0.9166666667x + x2 = 1 + 0.2100694445

Combine like terms: 1 + 0.2100694445 = 1.2100694445
0.2100694445 + -0.9166666667x + x2 = 1.2100694445

Factor a perfect square on the left side:
(x + -0.4583333334)(x + -0.4583333334) = 1.2100694445

Calculate the square root of the right side: 1.100031565

Break this problem into two subproblems by setting 
(x + -0.4583333334) equal to 1.100031565 and -1.100031565.

Subproblem 1
x + -0.4583333334 = 1.100031565

Simplifying
x + -0.4583333334 = 1.100031565

Reorder the terms:
-0.4583333334 + x = 1.100031565

Solving
-0.4583333334 + x = 1.100031565

Solving for variable 'x'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + x = 1.100031565 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + x = 1.100031565 + 0.4583333334
x = 1.100031565 + 0.4583333334

Combine like terms: 1.100031565 + 0.4583333334 = 1.5583648984
x = 1.5583648984

Simplifying
x = 1.5583648984

Subproblem 2
x + -0.4583333334 = -1.100031565

Simplifying
x + -0.4583333334 = -1.100031565

Reorder the terms:
-0.4583333334 + x = -1.100031565

Solving
-0.4583333334 + x = -1.100031565

Solving for variable 'x'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + x = -1.100031565 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + x = -1.100031565 + 0.4583333334
x = -1.100031565 + 0.4583333334

Combine like terms: -1.100031565 + 0.4583333334 = -0.6416982316
x = -0.6416982316

Simplifying
x = -0.6416982316

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5583648984, -0.6416982316}