22=6+34t-16t^2

Solution for 22=6+34t-16t^2 equation:

Simplifying
22 = 6 + 34t + -16t2

Solving
22 = 6 + 34t + -16t2

Solving for variable 't'.

Combine like terms: 22 + -6 = 16
16 + -34t + 16t2 = 6 + 34t + -16t2 + -6 + -34t + 16t2

Reorder the terms:
16 + -34t + 16t2 = 6 + -6 + 34t + -34t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
16 + -34t + 16t2 = 0 + 34t + -34t + -16t2 + 16t2
16 + -34t + 16t2 = 34t + -34t + -16t2 + 16t2

Combine like terms: 34t + -34t = 0
16 + -34t + 16t2 = 0 + -16t2 + 16t2
16 + -34t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
16 + -34t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -17t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -17t + 8t2)' equal to zero and attempt to solve:

Simplifying
8 + -17t + 8t2 = 0

Solving
8 + -17t + 8t2 = 0

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

Divide each side by '8'.
1 + -2.125t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.125t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -2.125t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.125t + t2 = 0 + -1
-2.125t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.125t + t2 = -1

The t term is -2.125t.  Take half its coefficient (-1.0625).
Square it (1.12890625) and add it to both sides.

Add '1.12890625' to each side of the equation.
-2.125t + 1.12890625 + t2 = -1 + 1.12890625

Reorder the terms:
1.12890625 + -2.125t + t2 = -1 + 1.12890625

Combine like terms: -1 + 1.12890625 = 0.12890625
1.12890625 + -2.125t + t2 = 0.12890625

Factor a perfect square on the left side:
(t + -1.0625)(t + -1.0625) = 0.12890625

Calculate the square root of the right side: 0.359035165

Break this problem into two subproblems by setting 
(t + -1.0625) equal to 0.359035165 and -0.359035165.

Subproblem 1
t + -1.0625 = 0.359035165

Simplifying
t + -1.0625 = 0.359035165

Reorder the terms:
-1.0625 + t = 0.359035165

Solving
-1.0625 + t = 0.359035165

Solving for variable 't'.

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

Add '1.0625' to each side of the equation.
-1.0625 + 1.0625 + t = 0.359035165 + 1.0625

Combine like terms: -1.0625 + 1.0625 = 0.0000
0.0000 + t = 0.359035165 + 1.0625
t = 0.359035165 + 1.0625

Combine like terms: 0.359035165 + 1.0625 = 1.421535165
t = 1.421535165

Simplifying
t = 1.421535165

Subproblem 2
t + -1.0625 = -0.359035165

Simplifying
t + -1.0625 = -0.359035165

Reorder the terms:
-1.0625 + t = -0.359035165

Solving
-1.0625 + t = -0.359035165

Solving for variable 't'.

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

Add '1.0625' to each side of the equation.
-1.0625 + 1.0625 + t = -0.359035165 + 1.0625

Combine like terms: -1.0625 + 1.0625 = 0.0000
0.0000 + t = -0.359035165 + 1.0625
t = -0.359035165 + 1.0625

Combine like terms: -0.359035165 + 1.0625 = 0.703464835
t = 0.703464835

Simplifying
t = 0.703464835

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.421535165, 0.703464835}
Solution
t = {1.421535165, 0.703464835}