-16t^2+20t+100=0

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Solution for -16t^2+20t+100=0 equation: 


Simplifying
-16t2 + 20t + 100 = 0

Reorder the terms:
100 + 20t + -16t2 = 0

Solving
100 + 20t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 5t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + 5t + -4t2)' equal to zero and attempt to solve:

Simplifying
25 + 5t + -4t2 = 0

Solving
25 + 5t + -4t2 = 0

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

Divide each side by '-4'.
-6.25 + -1.25t + t2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -1.25t + 6.25 + t2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -1.25t + t2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -1.25t + t2 = 0 + 6.25
-1.25t + t2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-1.25t + t2 = 6.25

The t term is -1.25t.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25t + 0.390625 + t2 = 6.25 + 0.390625

Reorder the terms:
0.390625 + -1.25t + t2 = 6.25 + 0.390625

Combine like terms: 6.25 + 0.390625 = 6.640625
0.390625 + -1.25t + t2 = 6.640625

Factor a perfect square on the left side:
(t + -0.625)(t + -0.625) = 6.640625

Calculate the square root of the right side: 2.576941016

Break this problem into two subproblems by setting 
(t + -0.625) equal to 2.576941016 and -2.576941016.


Subproblem 1
t + -0.625 = 2.576941016

Simplifying
t + -0.625 = 2.576941016

Reorder the terms:
-0.625 + t = 2.576941016

Solving
-0.625 + t = 2.576941016

Solving for variable 't'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + t = 2.576941016 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + t = 2.576941016 + 0.625
t = 2.576941016 + 0.625

Combine like terms: 2.576941016 + 0.625 = 3.201941016
t = 3.201941016

Simplifying
t = 3.201941016


Subproblem 2
t + -0.625 = -2.576941016

Simplifying
t + -0.625 = -2.576941016

Reorder the terms:
-0.625 + t = -2.576941016

Solving
-0.625 + t = -2.576941016

Solving for variable 't'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + t = -2.576941016 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + t = -2.576941016 + 0.625
t = -2.576941016 + 0.625

Combine like terms: -2.576941016 + 0.625 = -1.951941016
t = -1.951941016

Simplifying
t = -1.951941016


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.201941016, -1.951941016}
Solution
t = {3.201941016, -1.951941016}

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