x^2-144+12x+1=0

Solution for x^2-144+12x+1=0 equation:

Simplifying
x2 + -144 + 12x + 1 = 0

Reorder the terms:
-144 + 1 + 12x + x2 = 0

Combine like terms: -144 + 1 = -143
-143 + 12x + x2 = 0

Solving
-143 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '143' to each side of the equation.
-143 + 12x + 143 + x2 = 0 + 143

Reorder the terms:
-143 + 143 + 12x + x2 = 0 + 143

Combine like terms: -143 + 143 = 0
0 + 12x + x2 = 0 + 143
12x + x2 = 0 + 143

Combine like terms: 0 + 143 = 143
12x + x2 = 143

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 143 + 36

Reorder the terms:
36 + 12x + x2 = 143 + 36

Combine like terms: 143 + 36 = 179
36 + 12x + x2 = 179

Factor a perfect square on the left side:
(x + 6)(x + 6) = 179

Calculate the square root of the right side: 13.37908816

Break this problem into two subproblems by setting 
(x + 6) equal to 13.37908816 and -13.37908816.

Subproblem 1
x + 6 = 13.37908816

Simplifying
x + 6 = 13.37908816

Reorder the terms:
6 + x = 13.37908816

Solving
6 + x = 13.37908816

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 13.37908816 + -6

Combine like terms: 6 + -6 = 0
0 + x = 13.37908816 + -6
x = 13.37908816 + -6

Combine like terms: 13.37908816 + -6 = 7.37908816
x = 7.37908816

Simplifying
x = 7.37908816

Subproblem 2
x + 6 = -13.37908816

Simplifying
x + 6 = -13.37908816

Reorder the terms:
6 + x = -13.37908816

Solving
6 + x = -13.37908816

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -13.37908816 + -6

Combine like terms: 6 + -6 = 0
0 + x = -13.37908816 + -6
x = -13.37908816 + -6

Combine like terms: -13.37908816 + -6 = -19.37908816
x = -19.37908816

Simplifying
x = -19.37908816

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.37908816, -19.37908816}