t^2+6t+6=0

Solution for t^2+6t+6=0 equation:

Simplifying
t2 + 6t + 6 = 0

Reorder the terms:
6 + 6t + t2 = 0

Solving
6 + 6t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 6t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + 6t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 6t + t2 = 0 + -6
6t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
6t + t2 = -6

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

Add '9' to each side of the equation.
6t + 9 + t2 = -6 + 9

Reorder the terms:
9 + 6t + t2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + 6t + t2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(t + 3) equal to 1.732050808 and -1.732050808.

Subproblem 1
t + 3 = 1.732050808

Simplifying
t + 3 = 1.732050808

Reorder the terms:
3 + t = 1.732050808

Solving
3 + t = 1.732050808

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = 1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + t = 1.732050808 + -3
t = 1.732050808 + -3

Combine like terms: 1.732050808 + -3 = -1.267949192
t = -1.267949192

Simplifying
t = -1.267949192

Subproblem 2
t + 3 = -1.732050808

Simplifying
t + 3 = -1.732050808

Reorder the terms:
3 + t = -1.732050808

Solving
3 + t = -1.732050808

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = -1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + t = -1.732050808 + -3
t = -1.732050808 + -3

Combine like terms: -1.732050808 + -3 = -4.732050808
t = -4.732050808

Simplifying
t = -4.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.267949192, -4.732050808}