12x^2+x=14

Solution for 12x^2+x=14 equation:

Simplifying
12x2 + x = 14

Reorder the terms:
x + 12x2 = 14

Solving
x + 12x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + x + 12x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + x + 12x2 = 0

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

Divide each side by '12'.
-1.166666667 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 0.08333333333x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 0.08333333333x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 0.08333333333x + x2 = 0 + 1.166666667
0.08333333333x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
0.08333333333x + x2 = 1.166666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.08333333333x + 0.25 + x2 = 1.166666667 + 0.25

Reorder the terms:
0.25 + 0.08333333333x + x2 = 1.166666667 + 0.25

Combine like terms: 1.166666667 + 0.25 = 1.416666667
0.25 + 0.08333333333x + x2 = 1.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.416666667

Calculate the square root of the right side: 1.190238072

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.190238072 and -1.190238072.

Subproblem 1
x + 0.5 = 1.190238072

Simplifying
x + 0.5 = 1.190238072

Reorder the terms:
0.5 + x = 1.190238072

Solving
0.5 + x = 1.190238072

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.190238072 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.190238072 + -0.5
x = 1.190238072 + -0.5

Combine like terms: 1.190238072 + -0.5 = 0.690238072
x = 0.690238072

Simplifying
x = 0.690238072

Subproblem 2
x + 0.5 = -1.190238072

Simplifying
x + 0.5 = -1.190238072

Reorder the terms:
0.5 + x = -1.190238072

Solving
0.5 + x = -1.190238072

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.190238072 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.190238072 + -0.5
x = -1.190238072 + -0.5

Combine like terms: -1.190238072 + -0.5 = -1.690238072
x = -1.690238072

Simplifying
x = -1.690238072

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.690238072, -1.690238072}