-16t^2-4t+500=0

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Solution for -16t^2-4t+500=0 equation: 


Simplifying
-16t2 + -4t + 500 = 0

Reorder the terms:
500 + -4t + -16t2 = 0

Solving
500 + -4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(125 + -1t + -4t2) = 0

Ignore the factor 4.

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

Simplifying
125 + -1t + -4t2 = 0

Solving
125 + -1t + -4t2 = 0

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

Divide each side by '-4'.
-31.25 + 0.25t + t2 = 0

Move the constant term to the right:

Add '31.25' to each side of the equation.
-31.25 + 0.25t + 31.25 + t2 = 0 + 31.25

Reorder the terms:
-31.25 + 31.25 + 0.25t + t2 = 0 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + 0.25t + t2 = 0 + 31.25
0.25t + t2 = 0 + 31.25

Combine like terms: 0 + 31.25 = 31.25
0.25t + t2 = 31.25

The t term is 0.25t.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25t + 0.015625 + t2 = 31.25 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 31.25 + 0.015625

Combine like terms: 31.25 + 0.015625 = 31.265625
0.015625 + 0.25t + t2 = 31.265625

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 31.265625

Calculate the square root of the right side: 5.591567312

Break this problem into two subproblems by setting 
(t + 0.125) equal to 5.591567312 and -5.591567312.


Subproblem 1
t + 0.125 = 5.591567312

Simplifying
t + 0.125 = 5.591567312

Reorder the terms:
0.125 + t = 5.591567312

Solving
0.125 + t = 5.591567312

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = 5.591567312 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 5.591567312 + -0.125
t = 5.591567312 + -0.125

Combine like terms: 5.591567312 + -0.125 = 5.466567312
t = 5.466567312

Simplifying
t = 5.466567312


Subproblem 2
t + 0.125 = -5.591567312

Simplifying
t + 0.125 = -5.591567312

Reorder the terms:
0.125 + t = -5.591567312

Solving
0.125 + t = -5.591567312

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = -5.591567312 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -5.591567312 + -0.125
t = -5.591567312 + -0.125

Combine like terms: -5.591567312 + -0.125 = -5.716567312
t = -5.716567312

Simplifying
t = -5.716567312


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.466567312, -5.716567312}
Solution
t = {5.466567312, -5.716567312}

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