12x+x^2+3=0

Solution for 12x+x^2+3=0 equation:

Simplifying
12x + x2 + 3 = 0

Reorder the terms:
3 + 12x + x2 = 0

Solving
3 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 12x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 12x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 12x + x2 = 0 + -3
12x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
12x + x2 = -3

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 = -3 + 36

Reorder the terms:
36 + 12x + x2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + 12x + x2 = 33

Factor a perfect square on the left side:
(x + 6)(x + 6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + 6) equal to 5.744562647 and -5.744562647.

Subproblem 1
x + 6 = 5.744562647

Simplifying
x + 6 = 5.744562647

Reorder the terms:
6 + x = 5.744562647

Solving
6 + x = 5.744562647

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 = 5.744562647 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.744562647 + -6
x = 5.744562647 + -6

Combine like terms: 5.744562647 + -6 = -0.255437353
x = -0.255437353

Simplifying
x = -0.255437353

Subproblem 2
x + 6 = -5.744562647

Simplifying
x + 6 = -5.744562647

Reorder the terms:
6 + x = -5.744562647

Solving
6 + x = -5.744562647

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 = -5.744562647 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.744562647 + -6
x = -5.744562647 + -6

Combine like terms: -5.744562647 + -6 = -11.744562647
x = -11.744562647

Simplifying
x = -11.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.255437353, -11.744562647}