g^2+12g+7=0

Solution for g^2+12g+7=0 equation:

Simplifying
g2 + 12g + 7 = 0

Reorder the terms:
7 + 12g + g2 = 0

Solving
7 + 12g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 12g + -7 + g2 = 0 + -7

Reorder the terms:
7 + -7 + 12g + g2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 12g + g2 = 0 + -7
12g + g2 = 0 + -7

Combine like terms: 0 + -7 = -7
12g + g2 = -7

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

Add '36' to each side of the equation.
12g + 36 + g2 = -7 + 36

Reorder the terms:
36 + 12g + g2 = -7 + 36

Combine like terms: -7 + 36 = 29
36 + 12g + g2 = 29

Factor a perfect square on the left side:
(g + 6)(g + 6) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(g + 6) equal to 5.385164807 and -5.385164807.

Subproblem 1
g + 6 = 5.385164807

Simplifying
g + 6 = 5.385164807

Reorder the terms:
6 + g = 5.385164807

Solving
6 + g = 5.385164807

Solving for variable 'g'.

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

Add '-6' to each side of the equation.
6 + -6 + g = 5.385164807 + -6

Combine like terms: 6 + -6 = 0
0 + g = 5.385164807 + -6
g = 5.385164807 + -6

Combine like terms: 5.385164807 + -6 = -0.614835193
g = -0.614835193

Simplifying
g = -0.614835193

Subproblem 2
g + 6 = -5.385164807

Simplifying
g + 6 = -5.385164807

Reorder the terms:
6 + g = -5.385164807

Solving
6 + g = -5.385164807

Solving for variable 'g'.

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

Add '-6' to each side of the equation.
6 + -6 + g = -5.385164807 + -6

Combine like terms: 6 + -6 = 0
0 + g = -5.385164807 + -6
g = -5.385164807 + -6

Combine like terms: -5.385164807 + -6 = -11.385164807
g = -11.385164807

Simplifying
g = -11.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-0.614835193, -11.385164807}