0=-16t^2+16t+98

Solution for 0=-16t^2+16t+98 equation:

Simplifying
0 = -16t2 + 16t + 98

Reorder the terms:
0 = 98 + 16t + -16t2

Solving
0 = 98 + 16t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -98 = -98
-98 + -16t + 16t2 = 98 + 16t + -16t2 + -98 + -16t + 16t2

Reorder the terms:
-98 + -16t + 16t2 = 98 + -98 + 16t + -16t + -16t2 + 16t2

Combine like terms: 98 + -98 = 0
-98 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2
-98 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2

Combine like terms: 16t + -16t = 0
-98 + -16t + 16t2 = 0 + -16t2 + 16t2
-98 + -16t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-98 + -16t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + -8t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-49 + -8t + 8t2)' equal to zero and attempt to solve:

Simplifying
-49 + -8t + 8t2 = 0

Solving
-49 + -8t + 8t2 = 0

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

Divide each side by '8'.
-6.125 + -1t + t2 = 0

Move the constant term to the right:

Add '6.125' to each side of the equation.
-6.125 + -1t + 6.125 + t2 = 0 + 6.125

Reorder the terms:
-6.125 + 6.125 + -1t + t2 = 0 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + -1t + t2 = 0 + 6.125
-1t + t2 = 0 + 6.125

Combine like terms: 0 + 6.125 = 6.125
-1t + t2 = 6.125

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 6.125 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 6.125 + 0.25

Combine like terms: 6.125 + 0.25 = 6.375
0.25 + -1t + t2 = 6.375

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 6.375

Calculate the square root of the right side: 2.524876235

Break this problem into two subproblems by setting 
(t + -0.5) equal to 2.524876235 and -2.524876235.

Subproblem 1
t + -0.5 = 2.524876235

Simplifying
t + -0.5 = 2.524876235

Reorder the terms:
-0.5 + t = 2.524876235

Solving
-0.5 + t = 2.524876235

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 2.524876235 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 2.524876235 + 0.5
t = 2.524876235 + 0.5

Combine like terms: 2.524876235 + 0.5 = 3.024876235
t = 3.024876235

Simplifying
t = 3.024876235

Subproblem 2
t + -0.5 = -2.524876235

Simplifying
t + -0.5 = -2.524876235

Reorder the terms:
-0.5 + t = -2.524876235

Solving
-0.5 + t = -2.524876235

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -2.524876235 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -2.524876235 + 0.5
t = -2.524876235 + 0.5

Combine like terms: -2.524876235 + 0.5 = -2.024876235
t = -2.024876235

Simplifying
t = -2.024876235

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.024876235, -2.024876235}
Solution
t = {3.024876235, -2.024876235}