16t^2+50t+4=0

Solution for 16t^2+50t+4=0 equation:

Simplifying
16t2 + 50t + 4 = 0

Reorder the terms:
4 + 50t + 16t2 = 0

Solving
4 + 50t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 25t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 25t + 8t2)' equal to zero and attempt to solve:

Simplifying
2 + 25t + 8t2 = 0

Solving
2 + 25t + 8t2 = 0

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

Divide each side by '8'.
0.25 + 3.125t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 3.125t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 3.125t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 3.125t + t2 = 0 + -0.25
3.125t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
3.125t + t2 = -0.25

The t term is 3.125t.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125t + 2.44140625 + t2 = -0.25 + 2.44140625

Reorder the terms:
2.44140625 + 3.125t + t2 = -0.25 + 2.44140625

Combine like terms: -0.25 + 2.44140625 = 2.19140625
2.44140625 + 3.125t + t2 = 2.19140625

Factor a perfect square on the left side:
(t + 1.5625)(t + 1.5625) = 2.19140625

Calculate the square root of the right side: 1.48033991

Break this problem into two subproblems by setting 
(t + 1.5625) equal to 1.48033991 and -1.48033991.

Subproblem 1
t + 1.5625 = 1.48033991

Simplifying
t + 1.5625 = 1.48033991

Reorder the terms:
1.5625 + t = 1.48033991

Solving
1.5625 + t = 1.48033991

Solving for variable 't'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + t = 1.48033991 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + t = 1.48033991 + -1.5625
t = 1.48033991 + -1.5625

Combine like terms: 1.48033991 + -1.5625 = -0.08216009
t = -0.08216009

Simplifying
t = -0.08216009

Subproblem 2
t + 1.5625 = -1.48033991

Simplifying
t + 1.5625 = -1.48033991

Reorder the terms:
1.5625 + t = -1.48033991

Solving
1.5625 + t = -1.48033991

Solving for variable 't'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + t = -1.48033991 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + t = -1.48033991 + -1.5625
t = -1.48033991 + -1.5625

Combine like terms: -1.48033991 + -1.5625 = -3.04283991
t = -3.04283991

Simplifying
t = -3.04283991

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.08216009, -3.04283991}
Solution
t = {-0.08216009, -3.04283991}