122=16t^2+32t

Solution for 122=16t^2+32t equation:

Simplifying
122 = 16t2 + 32t

Reorder the terms:
122 = 32t + 16t2

Solving
122 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
122 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
122 + -32t + -16t2 = 0 + 16t2 + -16t2
122 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
122 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(61 + -16t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(61 + -16t + -8t2)' equal to zero and attempt to solve:

Simplifying
61 + -16t + -8t2 = 0

Solving
61 + -16t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-7.625 + 2t + t2 = 0

Move the constant term to the right:

Add '7.625' to each side of the equation.
-7.625 + 2t + 7.625 + t2 = 0 + 7.625

Reorder the terms:
-7.625 + 7.625 + 2t + t2 = 0 + 7.625

Combine like terms: -7.625 + 7.625 = 0.000
0.000 + 2t + t2 = 0 + 7.625
2t + t2 = 0 + 7.625

Combine like terms: 0 + 7.625 = 7.625
2t + t2 = 7.625

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 = 7.625 + 1

Reorder the terms:
1 + 2t + t2 = 7.625 + 1

Combine like terms: 7.625 + 1 = 8.625
1 + 2t + t2 = 8.625

Factor a perfect square on the left side:
(t + 1)(t + 1) = 8.625

Calculate the square root of the right side: 2.936835031

Break this problem into two subproblems by setting 
(t + 1) equal to 2.936835031 and -2.936835031.

Subproblem 1
t + 1 = 2.936835031

Simplifying
t + 1 = 2.936835031

Reorder the terms:
1 + t = 2.936835031

Solving
1 + t = 2.936835031

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 = 2.936835031 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.936835031 + -1
t = 2.936835031 + -1

Combine like terms: 2.936835031 + -1 = 1.936835031
t = 1.936835031

Simplifying
t = 1.936835031

Subproblem 2
t + 1 = -2.936835031

Simplifying
t + 1 = -2.936835031

Reorder the terms:
1 + t = -2.936835031

Solving
1 + t = -2.936835031

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 = -2.936835031 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.936835031 + -1
t = -2.936835031 + -1

Combine like terms: -2.936835031 + -1 = -3.936835031
t = -3.936835031

Simplifying
t = -3.936835031

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.936835031, -3.936835031}
Solution
t = {1.936835031, -3.936835031}