s^2+12s+25=0

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

Simplifying
s2 + 12s + 25 = 0

Reorder the terms:
25 + 12s + s2 = 0

Solving
25 + 12s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 12s + -25 + s2 = 0 + -25

Reorder the terms:
25 + -25 + 12s + s2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 12s + s2 = 0 + -25
12s + s2 = 0 + -25

Combine like terms: 0 + -25 = -25
12s + s2 = -25

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

Add '36' to each side of the equation.
12s + 36 + s2 = -25 + 36

Reorder the terms:
36 + 12s + s2 = -25 + 36

Combine like terms: -25 + 36 = 11
36 + 12s + s2 = 11

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

Calculate the square root of the right side: 3.31662479

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

Subproblem 1
s + 6 = 3.31662479

Simplifying
s + 6 = 3.31662479

Reorder the terms:
6 + s = 3.31662479

Solving
6 + s = 3.31662479

Solving for variable 's'.

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

Add '-6' to each side of the equation.
6 + -6 + s = 3.31662479 + -6

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

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

Simplifying
s = -2.68337521

Subproblem 2
s + 6 = -3.31662479

Simplifying
s + 6 = -3.31662479

Reorder the terms:
6 + s = -3.31662479

Solving
6 + s = -3.31662479

Solving for variable 's'.

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

Add '-6' to each side of the equation.
6 + -6 + s = -3.31662479 + -6

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

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

Simplifying
s = -9.31662479

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