-16t^2=45t+5

Solution for -16t^2=45t+5 equation:

Simplifying
-16t2 = 45t + 5

Reorder the terms:
-16t2 = 5 + 45t

Solving
-16t2 = 5 + 45t

Solving for variable 't'.

Reorder the terms:
-5 + -45t + -16t2 = 5 + 45t + -5 + -45t

Reorder the terms:
-5 + -45t + -16t2 = 5 + -5 + 45t + -45t

Combine like terms: 5 + -5 = 0
-5 + -45t + -16t2 = 0 + 45t + -45t
-5 + -45t + -16t2 = 45t + -45t

Combine like terms: 45t + -45t = 0
-5 + -45t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 45t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 45t + 16t2)' equal to zero and attempt to solve:

Simplifying
5 + 45t + 16t2 = 0

Solving
5 + 45t + 16t2 = 0

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

Divide each side by '16'.
0.3125 + 2.8125t + t2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 2.8125t + -0.3125 + t2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 2.8125t + t2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 2.8125t + t2 = 0 + -0.3125
2.8125t + t2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
2.8125t + t2 = -0.3125

The t term is 2.8125t.  Take half its coefficient (1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
2.8125t + 1.977539063 + t2 = -0.3125 + 1.977539063

Reorder the terms:
1.977539063 + 2.8125t + t2 = -0.3125 + 1.977539063

Combine like terms: -0.3125 + 1.977539063 = 1.665039063
1.977539063 + 2.8125t + t2 = 1.665039063

Factor a perfect square on the left side:
(t + 1.40625)(t + 1.40625) = 1.665039063

Calculate the square root of the right side: 1.290363927

Break this problem into two subproblems by setting 
(t + 1.40625) equal to 1.290363927 and -1.290363927.

Subproblem 1
t + 1.40625 = 1.290363927

Simplifying
t + 1.40625 = 1.290363927

Reorder the terms:
1.40625 + t = 1.290363927

Solving
1.40625 + t = 1.290363927

Solving for variable 't'.

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

Add '-1.40625' to each side of the equation.
1.40625 + -1.40625 + t = 1.290363927 + -1.40625

Combine like terms: 1.40625 + -1.40625 = 0.00000
0.00000 + t = 1.290363927 + -1.40625
t = 1.290363927 + -1.40625

Combine like terms: 1.290363927 + -1.40625 = -0.115886073
t = -0.115886073

Simplifying
t = -0.115886073

Subproblem 2
t + 1.40625 = -1.290363927

Simplifying
t + 1.40625 = -1.290363927

Reorder the terms:
1.40625 + t = -1.290363927

Solving
1.40625 + t = -1.290363927

Solving for variable 't'.

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

Add '-1.40625' to each side of the equation.
1.40625 + -1.40625 + t = -1.290363927 + -1.40625

Combine like terms: 1.40625 + -1.40625 = 0.00000
0.00000 + t = -1.290363927 + -1.40625
t = -1.290363927 + -1.40625

Combine like terms: -1.290363927 + -1.40625 = -2.696613927
t = -2.696613927

Simplifying
t = -2.696613927

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.115886073, -2.696613927}
Solution
t = {-0.115886073, -2.696613927}