a^2+6a+3=0

Solution for a^2+6a+3=0 equation:

Simplifying
a2 + 6a + 3 = 0

Reorder the terms:
3 + 6a + a2 = 0

Solving
3 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 6a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + 6a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 6a + a2 = 0 + -3
6a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
6a + a2 = -3

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = -3 + 9

Reorder the terms:
9 + 6a + a2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + 6a + a2 = 6

Factor a perfect square on the left side:
(a + 3)(a + 3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(a + 3) equal to 2.449489743 and -2.449489743.

Subproblem 1
a + 3 = 2.449489743

Simplifying
a + 3 = 2.449489743

Reorder the terms:
3 + a = 2.449489743

Solving
3 + a = 2.449489743

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = 2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + a = 2.449489743 + -3
a = 2.449489743 + -3

Combine like terms: 2.449489743 + -3 = -0.550510257
a = -0.550510257

Simplifying
a = -0.550510257

Subproblem 2
a + 3 = -2.449489743

Simplifying
a + 3 = -2.449489743

Reorder the terms:
3 + a = -2.449489743

Solving
3 + a = -2.449489743

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = -2.449489743 + -3

Combine like terms: 3 + -3 = 0
0 + a = -2.449489743 + -3
a = -2.449489743 + -3

Combine like terms: -2.449489743 + -3 = -5.449489743
a = -5.449489743

Simplifying
a = -5.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.550510257, -5.449489743}