109=12x+x^2

Solution for 109=12x+x^2 equation:

Simplifying
109 = 12x + x2

Solving
109 = 12x + x2

Solving for variable 'x'.

Reorder the terms:
109 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
109 + -12x + -1x2 = 0 + x2 + -1x2
109 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
109 + -12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-109 + 12x + x2 = 0

Move the constant term to the right:

Add '109' to each side of the equation.
-109 + 12x + 109 + x2 = 0 + 109

Reorder the terms:
-109 + 109 + 12x + x2 = 0 + 109

Combine like terms: -109 + 109 = 0
0 + 12x + x2 = 0 + 109
12x + x2 = 0 + 109

Combine like terms: 0 + 109 = 109
12x + x2 = 109

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 = 109 + 36

Reorder the terms:
36 + 12x + x2 = 109 + 36

Combine like terms: 109 + 36 = 145
36 + 12x + x2 = 145

Factor a perfect square on the left side:
(x + 6)(x + 6) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + 6) equal to 12.041594579 and -12.041594579.

Subproblem 1
x + 6 = 12.041594579

Simplifying
x + 6 = 12.041594579

Reorder the terms:
6 + x = 12.041594579

Solving
6 + x = 12.041594579

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 = 12.041594579 + -6

Combine like terms: 6 + -6 = 0
0 + x = 12.041594579 + -6
x = 12.041594579 + -6

Combine like terms: 12.041594579 + -6 = 6.041594579
x = 6.041594579

Simplifying
x = 6.041594579

Subproblem 2
x + 6 = -12.041594579

Simplifying
x + 6 = -12.041594579

Reorder the terms:
6 + x = -12.041594579

Solving
6 + x = -12.041594579

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 = -12.041594579 + -6

Combine like terms: 6 + -6 = 0
0 + x = -12.041594579 + -6
x = -12.041594579 + -6

Combine like terms: -12.041594579 + -6 = -18.041594579
x = -18.041594579

Simplifying
x = -18.041594579

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.041594579, -18.041594579}