-37=-11.9t-4.9t^2

Solution for -37=-11.9t-4.9t^2 equation:

Simplifying
-37 = -11.9t + -4.9t2

Solving
-37 = -11.9t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-37 + 11.9t + 4.9t2 = -11.9t + 11.9t + -4.9t2 + 4.9t2

Combine like terms: -11.9t + 11.9t = 0.0
-37 + 11.9t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-37 + 11.9t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-37 + 11.9t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
-7.551020408 + 2.428571429t + t2 = 0

Move the constant term to the right:

Add '7.551020408' to each side of the equation.
-7.551020408 + 2.428571429t + 7.551020408 + t2 = 0 + 7.551020408

Reorder the terms:
-7.551020408 + 7.551020408 + 2.428571429t + t2 = 0 + 7.551020408

Combine like terms: -7.551020408 + 7.551020408 = 0.000000000
0.000000000 + 2.428571429t + t2 = 0 + 7.551020408
2.428571429t + t2 = 0 + 7.551020408

Combine like terms: 0 + 7.551020408 = 7.551020408
2.428571429t + t2 = 7.551020408

The t term is 2.428571429t.  Take half its coefficient (1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
2.428571429t + 1.474489798 + t2 = 7.551020408 + 1.474489798

Reorder the terms:
1.474489798 + 2.428571429t + t2 = 7.551020408 + 1.474489798

Combine like terms: 7.551020408 + 1.474489798 = 9.025510206
1.474489798 + 2.428571429t + t2 = 9.025510206

Factor a perfect square on the left side:
(t + 1.214285715)(t + 1.214285715) = 9.025510206

Calculate the square root of the right side: 3.004248692

Break this problem into two subproblems by setting 
(t + 1.214285715) equal to 3.004248692 and -3.004248692.

Subproblem 1
t + 1.214285715 = 3.004248692

Simplifying
t + 1.214285715 = 3.004248692

Reorder the terms:
1.214285715 + t = 3.004248692

Solving
1.214285715 + t = 3.004248692

Solving for variable 't'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + t = 3.004248692 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + t = 3.004248692 + -1.214285715
t = 3.004248692 + -1.214285715

Combine like terms: 3.004248692 + -1.214285715 = 1.789962977
t = 1.789962977

Simplifying
t = 1.789962977

Subproblem 2
t + 1.214285715 = -3.004248692

Simplifying
t + 1.214285715 = -3.004248692

Reorder the terms:
1.214285715 + t = -3.004248692

Solving
1.214285715 + t = -3.004248692

Solving for variable 't'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + t = -3.004248692 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + t = -3.004248692 + -1.214285715
t = -3.004248692 + -1.214285715

Combine like terms: -3.004248692 + -1.214285715 = -4.218534407
t = -4.218534407

Simplifying
t = -4.218534407

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.789962977, -4.218534407}