12x^2-x-16=0

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Solution for 12x^2-x-16=0 equation: 


Simplifying
12x2 + -1x + -16 = 0

Reorder the terms:
-16 + -1x + 12x2 = 0

Solving
-16 + -1x + 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'.
-1.333333333 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.08333333333x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.08333333333x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.08333333333x + x2 = 0 + 1.333333333
-0.08333333333x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.08333333333x + x2 = 1.333333333

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 1.333333333 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 1.333333333 + 0.001736111111

Combine like terms: 1.333333333 + 0.001736111111 = 1.335069444111
0.001736111111 + -0.08333333333x + x2 = 1.335069444111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 1.335069444111

Calculate the square root of the right side: 1.155452052

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 1.155452052 and -1.155452052.


Subproblem 1
x + -0.04166666667 = 1.155452052

Simplifying
x + -0.04166666667 = 1.155452052

Reorder the terms:
-0.04166666667 + x = 1.155452052

Solving
-0.04166666667 + x = 1.155452052

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 1.155452052 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 1.155452052 + 0.04166666667
x = 1.155452052 + 0.04166666667

Combine like terms: 1.155452052 + 0.04166666667 = 1.19711871867
x = 1.19711871867

Simplifying
x = 1.19711871867


Subproblem 2
x + -0.04166666667 = -1.155452052

Simplifying
x + -0.04166666667 = -1.155452052

Reorder the terms:
-0.04166666667 + x = -1.155452052

Solving
-0.04166666667 + x = -1.155452052

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -1.155452052 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -1.155452052 + 0.04166666667
x = -1.155452052 + 0.04166666667

Combine like terms: -1.155452052 + 0.04166666667 = -1.11378538533
x = -1.11378538533

Simplifying
x = -1.11378538533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.19711871867, -1.11378538533}

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