-4.9t^2+16t-1=0

Solution for -4.9t^2+16t-1=0 equation:

Simplifying
-4.9t2 + 16t + -1 = 0

Reorder the terms:
-1 + 16t + -4.9t2 = 0

Solving
-1 + 16t + -4.9t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
0.2040816327 + -3.265306122t + t2 = 0

Move the constant term to the right:

Add '-0.2040816327' to each side of the equation.
0.2040816327 + -3.265306122t + -0.2040816327 + t2 = 0 + -0.2040816327

Reorder the terms:
0.2040816327 + -0.2040816327 + -3.265306122t + t2 = 0 + -0.2040816327

Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000
0.0000000000 + -3.265306122t + t2 = 0 + -0.2040816327
-3.265306122t + t2 = 0 + -0.2040816327

Combine like terms: 0 + -0.2040816327 = -0.2040816327
-3.265306122t + t2 = -0.2040816327

The t term is -3.265306122t.  Take half its coefficient (-1.632653061).
Square it (2.665556018) and add it to both sides.

Add '2.665556018' to each side of the equation.
-3.265306122t + 2.665556018 + t2 = -0.2040816327 + 2.665556018

Reorder the terms:
2.665556018 + -3.265306122t + t2 = -0.2040816327 + 2.665556018

Combine like terms: -0.2040816327 + 2.665556018 = 2.4614743853
2.665556018 + -3.265306122t + t2 = 2.4614743853

Factor a perfect square on the left side:
(t + -1.632653061)(t + -1.632653061) = 2.4614743853

Calculate the square root of the right side: 1.568908661

Break this problem into two subproblems by setting 
(t + -1.632653061) equal to 1.568908661 and -1.568908661.

Subproblem 1
t + -1.632653061 = 1.568908661

Simplifying
t + -1.632653061 = 1.568908661

Reorder the terms:
-1.632653061 + t = 1.568908661

Solving
-1.632653061 + t = 1.568908661

Solving for variable 't'.

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

Add '1.632653061' to each side of the equation.
-1.632653061 + 1.632653061 + t = 1.568908661 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + t = 1.568908661 + 1.632653061
t = 1.568908661 + 1.632653061

Combine like terms: 1.568908661 + 1.632653061 = 3.201561722
t = 3.201561722

Simplifying
t = 3.201561722

Subproblem 2
t + -1.632653061 = -1.568908661

Simplifying
t + -1.632653061 = -1.568908661

Reorder the terms:
-1.632653061 + t = -1.568908661

Solving
-1.632653061 + t = -1.568908661

Solving for variable 't'.

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

Add '1.632653061' to each side of the equation.
-1.632653061 + 1.632653061 + t = -1.568908661 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + t = -1.568908661 + 1.632653061
t = -1.568908661 + 1.632653061

Combine like terms: -1.568908661 + 1.632653061 = 0.0637444
t = 0.0637444

Simplifying
t = 0.0637444

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.201561722, 0.0637444}