0=x^2+12x+34

Solution for 0=x^2+12x+34 equation:

Simplifying
0 = x2 + 12x + 34

Reorder the terms:
0 = 34 + 12x + x2

Solving
0 = 34 + 12x + x2

Solving for variable 'x'.

Combine like terms: 0 + -34 = -34
-34 + -12x + -1x2 = 34 + 12x + x2 + -34 + -12x + -1x2

Reorder the terms:
-34 + -12x + -1x2 = 34 + -34 + 12x + -12x + x2 + -1x2

Combine like terms: 34 + -34 = 0
-34 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-34 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-34 + -12x + -1x2 = 0 + x2 + -1x2
-34 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-34 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(34 + 12x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(34 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
34 + 12x + x2 = 0

Solving
34 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + 12x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + 12x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + 12x + x2 = 0 + -34
12x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
12x + x2 = -34

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 = -34 + 36

Reorder the terms:
36 + 12x + x2 = -34 + 36

Combine like terms: -34 + 36 = 2
36 + 12x + x2 = 2

Factor a perfect square on the left side:
(x + 6)(x + 6) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 6) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + 6 = 1.414213562

Simplifying
x + 6 = 1.414213562

Reorder the terms:
6 + x = 1.414213562

Solving
6 + x = 1.414213562

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 = 1.414213562 + -6

Combine like terms: 6 + -6 = 0
0 + x = 1.414213562 + -6
x = 1.414213562 + -6

Combine like terms: 1.414213562 + -6 = -4.585786438
x = -4.585786438

Simplifying
x = -4.585786438

Subproblem 2
x + 6 = -1.414213562

Simplifying
x + 6 = -1.414213562

Reorder the terms:
6 + x = -1.414213562

Solving
6 + x = -1.414213562

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 = -1.414213562 + -6

Combine like terms: 6 + -6 = 0
0 + x = -1.414213562 + -6
x = -1.414213562 + -6

Combine like terms: -1.414213562 + -6 = -7.414213562
x = -7.414213562

Simplifying
x = -7.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.585786438, -7.414213562}
Solution
x = {-4.585786438, -7.414213562}