16t^2-40t+2=0

Solution for 16t^2-40t+2=0 equation:

Simplifying
16t2 + -40t + 2 = 0

Reorder the terms:
2 + -40t + 16t2 = 0

Solving
2 + -40t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -20t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -20t + 8t2)' equal to zero and attempt to solve:

Simplifying
1 + -20t + 8t2 = 0

Solving
1 + -20t + 8t2 = 0

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

Divide each side by '8'.
0.125 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -2.5t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -2.5t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -2.5t + t2 = 0 + -0.125
-2.5t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-2.5t + t2 = -0.125

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -0.125 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -0.125 + 1.5625

Combine like terms: -0.125 + 1.5625 = 1.4375
1.5625 + -2.5t + t2 = 1.4375

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 1.4375

Calculate the square root of the right side: 1.198957881

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.198957881 and -1.198957881.

Subproblem 1
t + -1.25 = 1.198957881

Simplifying
t + -1.25 = 1.198957881

Reorder the terms:
-1.25 + t = 1.198957881

Solving
-1.25 + t = 1.198957881

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 1.198957881 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 1.198957881 + 1.25
t = 1.198957881 + 1.25

Combine like terms: 1.198957881 + 1.25 = 2.448957881
t = 2.448957881

Simplifying
t = 2.448957881

Subproblem 2
t + -1.25 = -1.198957881

Simplifying
t + -1.25 = -1.198957881

Reorder the terms:
-1.25 + t = -1.198957881

Solving
-1.25 + t = -1.198957881

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -1.198957881 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -1.198957881 + 1.25
t = -1.198957881 + 1.25

Combine like terms: -1.198957881 + 1.25 = 0.051042119
t = 0.051042119

Simplifying
t = 0.051042119

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.448957881, 0.051042119}
Solution
t = {2.448957881, 0.051042119}