16t^2-32t+5=0

Solution for 16t^2-32t+5=0 equation:

Simplifying
16t2 + -32t + 5 = 0

Reorder the terms:
5 + -32t + 16t2 = 0

Solving
5 + -32t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
0.3125 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -2t + -0.3125 + t2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -2t + t2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -2t + t2 = 0 + -0.3125
-2t + t2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-2t + t2 = -0.3125

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 = -0.3125 + 1

Reorder the terms:
1 + -2t + t2 = -0.3125 + 1

Combine like terms: -0.3125 + 1 = 0.6875
1 + -2t + t2 = 0.6875

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(t + -1) equal to 0.829156198 and -0.829156198.

Subproblem 1
t + -1 = 0.829156198

Simplifying
t + -1 = 0.829156198

Reorder the terms:
-1 + t = 0.829156198

Solving
-1 + t = 0.829156198

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 = 0.829156198 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.829156198 + 1
t = 0.829156198 + 1

Combine like terms: 0.829156198 + 1 = 1.829156198
t = 1.829156198

Simplifying
t = 1.829156198

Subproblem 2
t + -1 = -0.829156198

Simplifying
t + -1 = -0.829156198

Reorder the terms:
-1 + t = -0.829156198

Solving
-1 + t = -0.829156198

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 = -0.829156198 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.829156198 + 1
t = -0.829156198 + 1

Combine like terms: -0.829156198 + 1 = 0.170843802
t = 0.170843802

Simplifying
t = 0.170843802

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.829156198, 0.170843802}