-16t^2+32t+5=1

Solution for -16t^2+32t+5=1 equation:

Simplifying
-16t2 + 32t + 5 = 1

Reorder the terms:
5 + 32t + -16t2 = 1

Solving
5 + 32t + -16t2 = 1

Solving for variable 't'.

Reorder the terms:
5 + -1 + 32t + -16t2 = 1 + -1

Combine like terms: 5 + -1 = 4
4 + 32t + -16t2 = 1 + -1

Combine like terms: 1 + -1 = 0
4 + 32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 8t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 8t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 8t + -4t2 = 0

Solving
1 + 8t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -2t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2t + t2 = 0 + 0.25
-2t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2t + t2 = 0.25

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 = 0.25 + 1

Reorder the terms:
1 + -2t + t2 = 0.25 + 1

Combine like terms: 0.25 + 1 = 1.25
1 + -2t + t2 = 1.25

Factor a perfect square on the left side:
(t + -1)(t + -1) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(t + -1) equal to 1.118033989 and -1.118033989.

Subproblem 1
t + -1 = 1.118033989

Simplifying
t + -1 = 1.118033989

Reorder the terms:
-1 + t = 1.118033989

Solving
-1 + t = 1.118033989

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 = 1.118033989 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.118033989 + 1
t = 1.118033989 + 1

Combine like terms: 1.118033989 + 1 = 2.118033989
t = 2.118033989

Simplifying
t = 2.118033989

Subproblem 2
t + -1 = -1.118033989

Simplifying
t + -1 = -1.118033989

Reorder the terms:
-1 + t = -1.118033989

Solving
-1 + t = -1.118033989

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 = -1.118033989 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.118033989 + 1
t = -1.118033989 + 1

Combine like terms: -1.118033989 + 1 = -0.118033989
t = -0.118033989

Simplifying
t = -0.118033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.118033989, -0.118033989}
Solution
t = {2.118033989, -0.118033989}