-16t^2+32t=1

Solution for -16t^2+32t=1 equation:

Simplifying
-16t2 + 32t = 1

Reorder the terms:
32t + -16t2 = 1

Solving
32t + -16t2 = 1

Solving for variable 't'.

Reorder the terms:
-1 + 32t + -16t2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 32t + -16t2 = 0

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

Divide each side by '-16'.
0.0625 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -2t + -0.0625 + t2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -2t + t2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -2t + t2 = 0 + -0.0625
-2t + t2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-2t + t2 = -0.0625

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 = -0.0625 + 1

Reorder the terms:
1 + -2t + t2 = -0.0625 + 1

Combine like terms: -0.0625 + 1 = 0.9375
1 + -2t + t2 = 0.9375

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(t + -1) equal to 0.968245837 and -0.968245837.

Subproblem 1
t + -1 = 0.968245837

Simplifying
t + -1 = 0.968245837

Reorder the terms:
-1 + t = 0.968245837

Solving
-1 + t = 0.968245837

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 = 0.968245837 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.968245837 + 1
t = 0.968245837 + 1

Combine like terms: 0.968245837 + 1 = 1.968245837
t = 1.968245837

Simplifying
t = 1.968245837

Subproblem 2
t + -1 = -0.968245837

Simplifying
t + -1 = -0.968245837

Reorder the terms:
-1 + t = -0.968245837

Solving
-1 + t = -0.968245837

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 = -0.968245837 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.968245837 + 1
t = -0.968245837 + 1

Combine like terms: -0.968245837 + 1 = 0.031754163
t = 0.031754163

Simplifying
t = 0.031754163

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.968245837, 0.031754163}