t^2+9t=-6

Solution for t^2+9t=-6 equation:

Simplifying
t2 + 9t = -6

Reorder the terms:
9t + t2 = -6

Solving
9t + t2 = -6

Solving for variable 't'.

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

Combine like terms: -6 + 6 = 0
6 + 9t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 9t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + 9t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 9t + t2 = 0 + -6
9t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
9t + t2 = -6

The t term is 9t.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9t + 20.25 + t2 = -6 + 20.25

Reorder the terms:
20.25 + 9t + t2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + 9t + t2 = 14.25

Factor a perfect square on the left side:
(t + 4.5)(t + 4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(t + 4.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
t + 4.5 = 3.774917218

Simplifying
t + 4.5 = 3.774917218

Reorder the terms:
4.5 + t = 3.774917218

Solving
4.5 + t = 3.774917218

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = 3.774917218 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = 3.774917218 + -4.5
t = 3.774917218 + -4.5

Combine like terms: 3.774917218 + -4.5 = -0.725082782
t = -0.725082782

Simplifying
t = -0.725082782

Subproblem 2
t + 4.5 = -3.774917218

Simplifying
t + 4.5 = -3.774917218

Reorder the terms:
4.5 + t = -3.774917218

Solving
4.5 + t = -3.774917218

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = -3.774917218 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = -3.774917218 + -4.5
t = -3.774917218 + -4.5

Combine like terms: -3.774917218 + -4.5 = -8.274917218
t = -8.274917218

Simplifying
t = -8.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.725082782, -8.274917218}