-16t^2-4t+470=0

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Solution for -16t^2-4t+470=0 equation: 


Simplifying
-16t2 + -4t + 470 = 0

Reorder the terms:
470 + -4t + -16t2 = 0

Solving
470 + -4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(235 + -2t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(235 + -2t + -8t2)' equal to zero and attempt to solve:

Simplifying
235 + -2t + -8t2 = 0

Solving
235 + -2t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-29.375 + 0.25t + t2 = 0

Move the constant term to the right:

Add '29.375' to each side of the equation.
-29.375 + 0.25t + 29.375 + t2 = 0 + 29.375

Reorder the terms:
-29.375 + 29.375 + 0.25t + t2 = 0 + 29.375

Combine like terms: -29.375 + 29.375 = 0.000
0.000 + 0.25t + t2 = 0 + 29.375
0.25t + t2 = 0 + 29.375

Combine like terms: 0 + 29.375 = 29.375
0.25t + t2 = 29.375

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 = 29.375 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 29.375 + 0.015625

Combine like terms: 29.375 + 0.015625 = 29.390625
0.015625 + 0.25t + t2 = 29.390625

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 29.390625

Calculate the square root of the right side: 5.421312111

Break this problem into two subproblems by setting 
(t + 0.125) equal to 5.421312111 and -5.421312111.


Subproblem 1
t + 0.125 = 5.421312111

Simplifying
t + 0.125 = 5.421312111

Reorder the terms:
0.125 + t = 5.421312111

Solving
0.125 + t = 5.421312111

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 = 5.421312111 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 5.421312111 + -0.125
t = 5.421312111 + -0.125

Combine like terms: 5.421312111 + -0.125 = 5.296312111
t = 5.296312111

Simplifying
t = 5.296312111


Subproblem 2
t + 0.125 = -5.421312111

Simplifying
t + 0.125 = -5.421312111

Reorder the terms:
0.125 + t = -5.421312111

Solving
0.125 + t = -5.421312111

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 = -5.421312111 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -5.421312111 + -0.125
t = -5.421312111 + -0.125

Combine like terms: -5.421312111 + -0.125 = -5.546312111
t = -5.546312111

Simplifying
t = -5.546312111


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.296312111, -5.546312111}
Solution
t = {5.296312111, -5.546312111}

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