16t^2+32t=77

Solution for 16t^2+32t=77 equation:

Simplifying
16t2 + 32t = 77

Reorder the terms:
32t + 16t2 = 77

Solving
32t + 16t2 = 77

Solving for variable 't'.

Reorder the terms:
-77 + 32t + 16t2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 32t + 16t2 = 0

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

Divide each side by '16'.
-4.8125 + 2t + t2 = 0

Move the constant term to the right:

Add '4.8125' to each side of the equation.
-4.8125 + 2t + 4.8125 + t2 = 0 + 4.8125

Reorder the terms:
-4.8125 + 4.8125 + 2t + t2 = 0 + 4.8125

Combine like terms: -4.8125 + 4.8125 = 0.0000
0.0000 + 2t + t2 = 0 + 4.8125
2t + t2 = 0 + 4.8125

Combine like terms: 0 + 4.8125 = 4.8125
2t + t2 = 4.8125

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 = 4.8125 + 1

Reorder the terms:
1 + 2t + t2 = 4.8125 + 1

Combine like terms: 4.8125 + 1 = 5.8125
1 + 2t + t2 = 5.8125

Factor a perfect square on the left side:
(t + 1)(t + 1) = 5.8125

Calculate the square root of the right side: 2.41091269

Break this problem into two subproblems by setting 
(t + 1) equal to 2.41091269 and -2.41091269.

Subproblem 1
t + 1 = 2.41091269

Simplifying
t + 1 = 2.41091269

Reorder the terms:
1 + t = 2.41091269

Solving
1 + t = 2.41091269

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 = 2.41091269 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.41091269 + -1
t = 2.41091269 + -1

Combine like terms: 2.41091269 + -1 = 1.41091269
t = 1.41091269

Simplifying
t = 1.41091269

Subproblem 2
t + 1 = -2.41091269

Simplifying
t + 1 = -2.41091269

Reorder the terms:
1 + t = -2.41091269

Solving
1 + t = -2.41091269

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 = -2.41091269 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.41091269 + -1
t = -2.41091269 + -1

Combine like terms: -2.41091269 + -1 = -3.41091269
t = -3.41091269

Simplifying
t = -3.41091269

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.41091269, -3.41091269}