x^2+12x+25=0

Solution for x^2+12x+25=0 equation:

Simplifying
x2 + 12x + 25 = 0

Reorder the terms:
25 + 12x + x2 = 0

Solving
25 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 12x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 12x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 12x + x2 = 0 + -25
12x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
12x + x2 = -25

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 = -25 + 36

Reorder the terms:
36 + 12x + x2 = -25 + 36

Combine like terms: -25 + 36 = 11
36 + 12x + x2 = 11

Factor a perfect square on the left side:
(x + 6)(x + 6) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 6) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + 6 = 3.31662479

Simplifying
x + 6 = 3.31662479

Reorder the terms:
6 + x = 3.31662479

Solving
6 + x = 3.31662479

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 = 3.31662479 + -6

Combine like terms: 6 + -6 = 0
0 + x = 3.31662479 + -6
x = 3.31662479 + -6

Combine like terms: 3.31662479 + -6 = -2.68337521
x = -2.68337521

Simplifying
x = -2.68337521

Subproblem 2
x + 6 = -3.31662479

Simplifying
x + 6 = -3.31662479

Reorder the terms:
6 + x = -3.31662479

Solving
6 + x = -3.31662479

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 = -3.31662479 + -6

Combine like terms: 6 + -6 = 0
0 + x = -3.31662479 + -6
x = -3.31662479 + -6

Combine like terms: -3.31662479 + -6 = -9.31662479
x = -9.31662479

Simplifying
x = -9.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.68337521, -9.31662479}