x^2+144x+121=0

Solution for x^2+144x+121=0 equation:

Simplifying
x2 + 144x + 121 = 0

Reorder the terms:
121 + 144x + x2 = 0

Solving
121 + 144x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-121' to each side of the equation.
121 + 144x + -121 + x2 = 0 + -121

Reorder the terms:
121 + -121 + 144x + x2 = 0 + -121

Combine like terms: 121 + -121 = 0
0 + 144x + x2 = 0 + -121
144x + x2 = 0 + -121

Combine like terms: 0 + -121 = -121
144x + x2 = -121

The x term is 144x.  Take half its coefficient (72).
Square it (5184) and add it to both sides.

Add '5184' to each side of the equation.
144x + 5184 + x2 = -121 + 5184

Reorder the terms:
5184 + 144x + x2 = -121 + 5184

Combine like terms: -121 + 5184 = 5063
5184 + 144x + x2 = 5063

Factor a perfect square on the left side:
(x + 72)(x + 72) = 5063

Calculate the square root of the right side: 71.154760909

Break this problem into two subproblems by setting 
(x + 72) equal to 71.154760909 and -71.154760909.

Subproblem 1
x + 72 = 71.154760909

Simplifying
x + 72 = 71.154760909

Reorder the terms:
72 + x = 71.154760909

Solving
72 + x = 71.154760909

Solving for variable 'x'.

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

Add '-72' to each side of the equation.
72 + -72 + x = 71.154760909 + -72

Combine like terms: 72 + -72 = 0
0 + x = 71.154760909 + -72
x = 71.154760909 + -72

Combine like terms: 71.154760909 + -72 = -0.845239091
x = -0.845239091

Simplifying
x = -0.845239091

Subproblem 2
x + 72 = -71.154760909

Simplifying
x + 72 = -71.154760909

Reorder the terms:
72 + x = -71.154760909

Solving
72 + x = -71.154760909

Solving for variable 'x'.

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

Add '-72' to each side of the equation.
72 + -72 + x = -71.154760909 + -72

Combine like terms: 72 + -72 = 0
0 + x = -71.154760909 + -72
x = -71.154760909 + -72

Combine like terms: -71.154760909 + -72 = -143.154760909
x = -143.154760909

Simplifying
x = -143.154760909

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.845239091, -143.154760909}