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

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


Simplifying
-16t2 + 100t + 16 = 0

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

Solving
16 + 100t + -16t2 = 0

Solving for variable 't'.

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

Ignore the factor 4.

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

Simplifying
4 + 25t + -4t2 = 0

Solving
4 + 25t + -4t2 = 0

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

Divide each side by '-4'.
-1 + -6.25t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6.25t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -6.25t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6.25t + t2 = 0 + 1
-6.25t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6.25t + t2 = 1

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 = 1 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = 1 + 9.765625

Combine like terms: 1 + 9.765625 = 10.765625
9.765625 + -6.25t + t2 = 10.765625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 10.765625

Calculate the square root of the right side: 3.281101187

Break this problem into two subproblems by setting 
(t + -3.125) equal to 3.281101187 and -3.281101187.


Subproblem 1
t + -3.125 = 3.281101187

Simplifying
t + -3.125 = 3.281101187

Reorder the terms:
-3.125 + t = 3.281101187

Solving
-3.125 + t = 3.281101187

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 = 3.281101187 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = 3.281101187 + 3.125
t = 3.281101187 + 3.125

Combine like terms: 3.281101187 + 3.125 = 6.406101187
t = 6.406101187

Simplifying
t = 6.406101187


Subproblem 2
t + -3.125 = -3.281101187

Simplifying
t + -3.125 = -3.281101187

Reorder the terms:
-3.125 + t = -3.281101187

Solving
-3.125 + t = -3.281101187

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 = -3.281101187 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = -3.281101187 + 3.125
t = -3.281101187 + 3.125

Combine like terms: -3.281101187 + 3.125 = -0.156101187
t = -0.156101187

Simplifying
t = -0.156101187


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.406101187, -0.156101187}
Solution
t = {6.406101187, -0.156101187}

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