x^2-12x-144=0

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

Simplifying
x2 + -12x + -144 = 0

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

Solving
-144 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -12x + 144 + x2 = 0 + 144

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

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

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

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 = 144 + 36

Reorder the terms:
36 + -12x + x2 = 144 + 36

Combine like terms: 144 + 36 = 180
36 + -12x + x2 = 180

Factor a perfect square on the left side:
(x + -6)(x + -6) = 180

Calculate the square root of the right side: 13.416407865

Break this problem into two subproblems by setting 
(x + -6) equal to 13.416407865 and -13.416407865.

Subproblem 1
x + -6 = 13.416407865

Simplifying
x + -6 = 13.416407865

Reorder the terms:
-6 + x = 13.416407865

Solving
-6 + x = 13.416407865

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 = 13.416407865 + 6

Combine like terms: -6 + 6 = 0
0 + x = 13.416407865 + 6
x = 13.416407865 + 6

Combine like terms: 13.416407865 + 6 = 19.416407865
x = 19.416407865

Simplifying
x = 19.416407865

Subproblem 2
x + -6 = -13.416407865

Simplifying
x + -6 = -13.416407865

Reorder the terms:
-6 + x = -13.416407865

Solving
-6 + x = -13.416407865

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 = -13.416407865 + 6

Combine like terms: -6 + 6 = 0
0 + x = -13.416407865 + 6
x = -13.416407865 + 6

Combine like terms: -13.416407865 + 6 = -7.416407865
x = -7.416407865

Simplifying
x = -7.416407865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.416407865, -7.416407865}