12x^2-4x-207=0

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Solution for 12x^2-4x-207=0 equation: 


Simplifying
12x2 + -4x + -207 = 0

Reorder the terms:
-207 + -4x + 12x2 = 0

Solving
-207 + -4x + 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'.
-17.25 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '17.25' to each side of the equation.
-17.25 + -0.3333333333x + 17.25 + x2 = 0 + 17.25

Reorder the terms:
-17.25 + 17.25 + -0.3333333333x + x2 = 0 + 17.25

Combine like terms: -17.25 + 17.25 = 0.00
0.00 + -0.3333333333x + x2 = 0 + 17.25
-0.3333333333x + x2 = 0 + 17.25

Combine like terms: 0 + 17.25 = 17.25
-0.3333333333x + x2 = 17.25

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 17.25 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 17.25 + 0.02777777779

Combine like terms: 17.25 + 0.02777777779 = 17.27777777779
0.02777777779 + -0.3333333333x + x2 = 17.27777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 17.27777777779

Calculate the square root of the right side: 4.156654638

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 4.156654638 and -4.156654638.


Subproblem 1
x + -0.1666666667 = 4.156654638

Simplifying
x + -0.1666666667 = 4.156654638

Reorder the terms:
-0.1666666667 + x = 4.156654638

Solving
-0.1666666667 + x = 4.156654638

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 4.156654638 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 4.156654638 + 0.1666666667
x = 4.156654638 + 0.1666666667

Combine like terms: 4.156654638 + 0.1666666667 = 4.3233213047
x = 4.3233213047

Simplifying
x = 4.3233213047


Subproblem 2
x + -0.1666666667 = -4.156654638

Simplifying
x + -0.1666666667 = -4.156654638

Reorder the terms:
-0.1666666667 + x = -4.156654638

Solving
-0.1666666667 + x = -4.156654638

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -4.156654638 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -4.156654638 + 0.1666666667
x = -4.156654638 + 0.1666666667

Combine like terms: -4.156654638 + 0.1666666667 = -3.9899879713
x = -3.9899879713

Simplifying
x = -3.9899879713


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.3233213047, -3.9899879713}

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