16t^2-500t-300=0

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Solution for 16t^2-500t-300=0 equation: 


Simplifying
16t2 + -500t + -300 = 0

Reorder the terms:
-300 + -500t + 16t2 = 0

Solving
-300 + -500t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-75 + -125t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-75 + -125t + 4t2)' equal to zero and attempt to solve:

Simplifying
-75 + -125t + 4t2 = 0

Solving
-75 + -125t + 4t2 = 0

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

Divide each side by '4'.
-18.75 + -31.25t + t2 = 0

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + -31.25t + 18.75 + t2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + -31.25t + t2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + -31.25t + t2 = 0 + 18.75
-31.25t + t2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
-31.25t + t2 = 18.75

The t term is -31.25t.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25t + 244.140625 + t2 = 18.75 + 244.140625

Reorder the terms:
244.140625 + -31.25t + t2 = 18.75 + 244.140625

Combine like terms: 18.75 + 244.140625 = 262.890625
244.140625 + -31.25t + t2 = 262.890625

Factor a perfect square on the left side:
(t + -15.625)(t + -15.625) = 262.890625

Calculate the square root of the right side: 16.213902214

Break this problem into two subproblems by setting 
(t + -15.625) equal to 16.213902214 and -16.213902214.


Subproblem 1
t + -15.625 = 16.213902214

Simplifying
t + -15.625 = 16.213902214

Reorder the terms:
-15.625 + t = 16.213902214

Solving
-15.625 + t = 16.213902214

Solving for variable 't'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + t = 16.213902214 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + t = 16.213902214 + 15.625
t = 16.213902214 + 15.625

Combine like terms: 16.213902214 + 15.625 = 31.838902214
t = 31.838902214

Simplifying
t = 31.838902214


Subproblem 2
t + -15.625 = -16.213902214

Simplifying
t + -15.625 = -16.213902214

Reorder the terms:
-15.625 + t = -16.213902214

Solving
-15.625 + t = -16.213902214

Solving for variable 't'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + t = -16.213902214 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + t = -16.213902214 + 15.625
t = -16.213902214 + 15.625

Combine like terms: -16.213902214 + 15.625 = -0.588902214
t = -0.588902214

Simplifying
t = -0.588902214


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {31.838902214, -0.588902214}
Solution
t = {31.838902214, -0.588902214}

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