37000=28t^2+194t+9058

Solution for 37000=28t^2+194t+9058 equation:

Simplifying
37000 = 28t2 + 194t + 9058

Reorder the terms:
37000 = 9058 + 194t + 28t2

Solving
37000 = 9058 + 194t + 28t2

Solving for variable 't'.

Combine like terms: 37000 + -9058 = 27942
27942 + -194t + -28t2 = 9058 + 194t + 28t2 + -9058 + -194t + -28t2

Reorder the terms:
27942 + -194t + -28t2 = 9058 + -9058 + 194t + -194t + 28t2 + -28t2

Combine like terms: 9058 + -9058 = 0
27942 + -194t + -28t2 = 0 + 194t + -194t + 28t2 + -28t2
27942 + -194t + -28t2 = 194t + -194t + 28t2 + -28t2

Combine like terms: 194t + -194t = 0
27942 + -194t + -28t2 = 0 + 28t2 + -28t2
27942 + -194t + -28t2 = 28t2 + -28t2

Combine like terms: 28t2 + -28t2 = 0
27942 + -194t + -28t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13971 + -97t + -14t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13971 + -97t + -14t2)' equal to zero and attempt to solve:

Simplifying
13971 + -97t + -14t2 = 0

Solving
13971 + -97t + -14t2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-997.9285714 + 6.928571429t + t2 = 0

Move the constant term to the right:

Add '997.9285714' to each side of the equation.
-997.9285714 + 6.928571429t + 997.9285714 + t2 = 0 + 997.9285714

Reorder the terms:
-997.9285714 + 997.9285714 + 6.928571429t + t2 = 0 + 997.9285714

Combine like terms: -997.9285714 + 997.9285714 = 0.0000000
0.0000000 + 6.928571429t + t2 = 0 + 997.9285714
6.928571429t + t2 = 0 + 997.9285714

Combine like terms: 0 + 997.9285714 = 997.9285714
6.928571429t + t2 = 997.9285714

The t term is 6.928571429t.  Take half its coefficient (3.464285715).
Square it (12.00127552) and add it to both sides.

Add '12.00127552' to each side of the equation.
6.928571429t + 12.00127552 + t2 = 997.9285714 + 12.00127552

Reorder the terms:
12.00127552 + 6.928571429t + t2 = 997.9285714 + 12.00127552

Combine like terms: 997.9285714 + 12.00127552 = 1009.92984692
12.00127552 + 6.928571429t + t2 = 1009.92984692

Factor a perfect square on the left side:
(t + 3.464285715)(t + 3.464285715) = 1009.92984692

Calculate the square root of the right side: 31.779393432

Break this problem into two subproblems by setting 
(t + 3.464285715) equal to 31.779393432 and -31.779393432.

Subproblem 1
t + 3.464285715 = 31.779393432

Simplifying
t + 3.464285715 = 31.779393432

Reorder the terms:
3.464285715 + t = 31.779393432

Solving
3.464285715 + t = 31.779393432

Solving for variable 't'.

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

Add '-3.464285715' to each side of the equation.
3.464285715 + -3.464285715 + t = 31.779393432 + -3.464285715

Combine like terms: 3.464285715 + -3.464285715 = 0.000000000
0.000000000 + t = 31.779393432 + -3.464285715
t = 31.779393432 + -3.464285715

Combine like terms: 31.779393432 + -3.464285715 = 28.315107717
t = 28.315107717

Simplifying
t = 28.315107717

Subproblem 2
t + 3.464285715 = -31.779393432

Simplifying
t + 3.464285715 = -31.779393432

Reorder the terms:
3.464285715 + t = -31.779393432

Solving
3.464285715 + t = -31.779393432

Solving for variable 't'.

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

Add '-3.464285715' to each side of the equation.
3.464285715 + -3.464285715 + t = -31.779393432 + -3.464285715

Combine like terms: 3.464285715 + -3.464285715 = 0.000000000
0.000000000 + t = -31.779393432 + -3.464285715
t = -31.779393432 + -3.464285715

Combine like terms: -31.779393432 + -3.464285715 = -35.243679147
t = -35.243679147

Simplifying
t = -35.243679147

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {28.315107717, -35.243679147}
Solution
t = {28.315107717, -35.243679147}