5t^2+6t-44=0

Solution for 5t^2+6t-44=0 equation:

Simplifying
5t2 + 6t + -44 = 0

Reorder the terms:
-44 + 6t + 5t2 = 0

Solving
-44 + 6t + 5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-8.8 + 1.2t + t2 = 0

Move the constant term to the right:

Add '8.8' to each side of the equation.
-8.8 + 1.2t + 8.8 + t2 = 0 + 8.8

Reorder the terms:
-8.8 + 8.8 + 1.2t + t2 = 0 + 8.8

Combine like terms: -8.8 + 8.8 = 0.0
0.0 + 1.2t + t2 = 0 + 8.8
1.2t + t2 = 0 + 8.8

Combine like terms: 0 + 8.8 = 8.8
1.2t + t2 = 8.8

The t term is 1.2t.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2t + 0.36 + t2 = 8.8 + 0.36

Reorder the terms:
0.36 + 1.2t + t2 = 8.8 + 0.36

Combine like terms: 8.8 + 0.36 = 9.16
0.36 + 1.2t + t2 = 9.16

Factor a perfect square on the left side:
(t + 0.6)(t + 0.6) = 9.16

Calculate the square root of the right side: 3.02654919

Break this problem into two subproblems by setting 
(t + 0.6) equal to 3.02654919 and -3.02654919.

Subproblem 1
t + 0.6 = 3.02654919

Simplifying
t + 0.6 = 3.02654919

Reorder the terms:
0.6 + t = 3.02654919

Solving
0.6 + t = 3.02654919

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = 3.02654919 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = 3.02654919 + -0.6
t = 3.02654919 + -0.6

Combine like terms: 3.02654919 + -0.6 = 2.42654919
t = 2.42654919

Simplifying
t = 2.42654919

Subproblem 2
t + 0.6 = -3.02654919

Simplifying
t + 0.6 = -3.02654919

Reorder the terms:
0.6 + t = -3.02654919

Solving
0.6 + t = -3.02654919

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = -3.02654919 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = -3.02654919 + -0.6
t = -3.02654919 + -0.6

Combine like terms: -3.02654919 + -0.6 = -3.62654919
t = -3.62654919

Simplifying
t = -3.62654919

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.42654919, -3.62654919}