12x^2-2x-63=0

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Solution for 12x^2-2x-63=0 equation: 


Simplifying
12x2 + -2x + -63 = 0

Reorder the terms:
-63 + -2x + 12x2 = 0

Solving
-63 + -2x + 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'.
-5.25 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -0.1666666667x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -0.1666666667x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -0.1666666667x + x2 = 0 + 5.25
-0.1666666667x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-0.1666666667x + x2 = 5.25

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 5.25 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 5.25 + 0.006944444447

Combine like terms: 5.25 + 0.006944444447 = 5.256944444447
0.006944444447 + -0.1666666667x + x2 = 5.256944444447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 5.256944444447

Calculate the square root of the right side: 2.292802749

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 2.292802749 and -2.292802749.


Subproblem 1
x + -0.08333333335 = 2.292802749

Simplifying
x + -0.08333333335 = 2.292802749

Reorder the terms:
-0.08333333335 + x = 2.292802749

Solving
-0.08333333335 + x = 2.292802749

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 2.292802749 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 2.292802749 + 0.08333333335
x = 2.292802749 + 0.08333333335

Combine like terms: 2.292802749 + 0.08333333335 = 2.37613608235
x = 2.37613608235

Simplifying
x = 2.37613608235


Subproblem 2
x + -0.08333333335 = -2.292802749

Simplifying
x + -0.08333333335 = -2.292802749

Reorder the terms:
-0.08333333335 + x = -2.292802749

Solving
-0.08333333335 + x = -2.292802749

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -2.292802749 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -2.292802749 + 0.08333333335
x = -2.292802749 + 0.08333333335

Combine like terms: -2.292802749 + 0.08333333335 = -2.20946941565
x = -2.20946941565

Simplifying
x = -2.20946941565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.37613608235, -2.20946941565}

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