-16t^2-100t+100000=0

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Solution for -16t^2-100t+100000=0 equation: 


Simplifying
-16t2 + -100t + 100000 = 0

Reorder the terms:
100000 + -100t + -16t2 = 0

Solving
100000 + -100t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25000 + -25t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25000 + -25t + -4t2)' equal to zero and attempt to solve:

Simplifying
25000 + -25t + -4t2 = 0

Solving
25000 + -25t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-6250 + 6.25t + t2 = 0

Move the constant term to the right:

Add '6250' to each side of the equation.
-6250 + 6.25t + 6250 + t2 = 0 + 6250

Reorder the terms:
-6250 + 6250 + 6.25t + t2 = 0 + 6250

Combine like terms: -6250 + 6250 = 0
0 + 6.25t + t2 = 0 + 6250
6.25t + t2 = 0 + 6250

Combine like terms: 0 + 6250 = 6250
6.25t + t2 = 6250

The t term is 6.25t.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25t + 9.765625 + t2 = 6250 + 9.765625

Reorder the terms:
9.765625 + 6.25t + t2 = 6250 + 9.765625

Combine like terms: 6250 + 9.765625 = 6259.765625
9.765625 + 6.25t + t2 = 6259.765625

Factor a perfect square on the left side:
(t + 3.125)(t + 3.125) = 6259.765625

Calculate the square root of the right side: 79.118680632

Break this problem into two subproblems by setting 
(t + 3.125) equal to 79.118680632 and -79.118680632.


Subproblem 1
t + 3.125 = 79.118680632

Simplifying
t + 3.125 = 79.118680632

Reorder the terms:
3.125 + t = 79.118680632

Solving
3.125 + t = 79.118680632

Solving for variable 't'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + t = 79.118680632 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = 79.118680632 + -3.125
t = 79.118680632 + -3.125

Combine like terms: 79.118680632 + -3.125 = 75.993680632
t = 75.993680632

Simplifying
t = 75.993680632


Subproblem 2
t + 3.125 = -79.118680632

Simplifying
t + 3.125 = -79.118680632

Reorder the terms:
3.125 + t = -79.118680632

Solving
3.125 + t = -79.118680632

Solving for variable 't'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + t = -79.118680632 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = -79.118680632 + -3.125
t = -79.118680632 + -3.125

Combine like terms: -79.118680632 + -3.125 = -82.243680632
t = -82.243680632

Simplifying
t = -82.243680632


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {75.993680632, -82.243680632}
Solution
t = {75.993680632, -82.243680632}

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