-16t^2-4t+472=0

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Solution for -16t^2-4t+472=0 equation: 


Simplifying
-16t2 + -4t + 472 = 0

Reorder the terms:
472 + -4t + -16t2 = 0

Solving
472 + -4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(118 + -1t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(118 + -1t + -4t2)' equal to zero and attempt to solve:

Simplifying
118 + -1t + -4t2 = 0

Solving
118 + -1t + -4t2 = 0

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

Divide each side by '-4'.
-29.5 + 0.25t + t2 = 0

Move the constant term to the right:

Add '29.5' to each side of the equation.
-29.5 + 0.25t + 29.5 + t2 = 0 + 29.5

Reorder the terms:
-29.5 + 29.5 + 0.25t + t2 = 0 + 29.5

Combine like terms: -29.5 + 29.5 = 0.0
0.0 + 0.25t + t2 = 0 + 29.5
0.25t + t2 = 0 + 29.5

Combine like terms: 0 + 29.5 = 29.5
0.25t + t2 = 29.5

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 = 29.5 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 29.5 + 0.015625

Combine like terms: 29.5 + 0.015625 = 29.515625
0.015625 + 0.25t + t2 = 29.515625

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 29.515625

Calculate the square root of the right side: 5.432828453

Break this problem into two subproblems by setting 
(t + 0.125) equal to 5.432828453 and -5.432828453.


Subproblem 1
t + 0.125 = 5.432828453

Simplifying
t + 0.125 = 5.432828453

Reorder the terms:
0.125 + t = 5.432828453

Solving
0.125 + t = 5.432828453

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 = 5.432828453 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 5.432828453 + -0.125
t = 5.432828453 + -0.125

Combine like terms: 5.432828453 + -0.125 = 5.307828453
t = 5.307828453

Simplifying
t = 5.307828453


Subproblem 2
t + 0.125 = -5.432828453

Simplifying
t + 0.125 = -5.432828453

Reorder the terms:
0.125 + t = -5.432828453

Solving
0.125 + t = -5.432828453

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 = -5.432828453 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -5.432828453 + -0.125
t = -5.432828453 + -0.125

Combine like terms: -5.432828453 + -0.125 = -5.557828453
t = -5.557828453

Simplifying
t = -5.557828453


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.307828453, -5.557828453}
Solution
t = {5.307828453, -5.557828453}

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