244=16t^2+32t

Solution for 244=16t^2+32t equation:

Simplifying
244 = 16t2 + 32t

Reorder the terms:
244 = 32t + 16t2

Solving
244 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
244 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
244 + -32t + -16t2 = 0 + 16t2 + -16t2
244 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
244 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(61 + -8t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(61 + -8t + -4t2)' equal to zero and attempt to solve:

Simplifying
61 + -8t + -4t2 = 0

Solving
61 + -8t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-15.25 + 2t + t2 = 0

Move the constant term to the right:

Add '15.25' to each side of the equation.
-15.25 + 2t + 15.25 + t2 = 0 + 15.25

Reorder the terms:
-15.25 + 15.25 + 2t + t2 = 0 + 15.25

Combine like terms: -15.25 + 15.25 = 0.00
0.00 + 2t + t2 = 0 + 15.25
2t + t2 = 0 + 15.25

Combine like terms: 0 + 15.25 = 15.25
2t + t2 = 15.25

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 15.25 + 1

Reorder the terms:
1 + 2t + t2 = 15.25 + 1

Combine like terms: 15.25 + 1 = 16.25
1 + 2t + t2 = 16.25

Factor a perfect square on the left side:
(t + 1)(t + 1) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(t + 1) equal to 4.031128874 and -4.031128874.

Subproblem 1
t + 1 = 4.031128874

Simplifying
t + 1 = 4.031128874

Reorder the terms:
1 + t = 4.031128874

Solving
1 + t = 4.031128874

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 4.031128874 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4.031128874 + -1
t = 4.031128874 + -1

Combine like terms: 4.031128874 + -1 = 3.031128874
t = 3.031128874

Simplifying
t = 3.031128874

Subproblem 2
t + 1 = -4.031128874

Simplifying
t + 1 = -4.031128874

Reorder the terms:
1 + t = -4.031128874

Solving
1 + t = -4.031128874

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -4.031128874 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4.031128874 + -1
t = -4.031128874 + -1

Combine like terms: -4.031128874 + -1 = -5.031128874
t = -5.031128874

Simplifying
t = -5.031128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.031128874, -5.031128874}
Solution
t = {3.031128874, -5.031128874}