t^6-49t^5-308t^4=0

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Solution for t^6-49t^5-308t^4=0 equation: 


Simplifying
t6 + -49t5 + -308t4 = 0

Reorder the terms:
-308t4 + -49t5 + t6 = 0

Solving
-308t4 + -49t5 + t6 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't4'.
t4(-308 + -49t + t2) = 0


Subproblem 1
Set the factor 't4' equal to zero and attempt to solve:

Simplifying
t4 = 0

Solving
t4 = 0

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

Simplifying
t4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-308 + -49t + t2)' equal to zero and attempt to solve:

Simplifying
-308 + -49t + t2 = 0

Solving
-308 + -49t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '308' to each side of the equation.
-308 + -49t + 308 + t2 = 0 + 308

Reorder the terms:
-308 + 308 + -49t + t2 = 0 + 308

Combine like terms: -308 + 308 = 0
0 + -49t + t2 = 0 + 308
-49t + t2 = 0 + 308

Combine like terms: 0 + 308 = 308
-49t + t2 = 308

The t term is -49t.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49t + 600.25 + t2 = 308 + 600.25

Reorder the terms:
600.25 + -49t + t2 = 308 + 600.25

Combine like terms: 308 + 600.25 = 908.25
600.25 + -49t + t2 = 908.25

Factor a perfect square on the left side:
(t + -24.5)(t + -24.5) = 908.25

Calculate the square root of the right side: 30.137186332

Break this problem into two subproblems by setting 
(t + -24.5) equal to 30.137186332 and -30.137186332.


Subproblem 1
t + -24.5 = 30.137186332

Simplifying
t + -24.5 = 30.137186332

Reorder the terms:
-24.5 + t = 30.137186332

Solving
-24.5 + t = 30.137186332

Solving for variable 't'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + t = 30.137186332 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + t = 30.137186332 + 24.5
t = 30.137186332 + 24.5

Combine like terms: 30.137186332 + 24.5 = 54.637186332
t = 54.637186332

Simplifying
t = 54.637186332


Subproblem 2
t + -24.5 = -30.137186332

Simplifying
t + -24.5 = -30.137186332

Reorder the terms:
-24.5 + t = -30.137186332

Solving
-24.5 + t = -30.137186332

Solving for variable 't'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + t = -30.137186332 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + t = -30.137186332 + 24.5
t = -30.137186332 + 24.5

Combine like terms: -30.137186332 + 24.5 = -5.637186332
t = -5.637186332

Simplifying
t = -5.637186332


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {54.637186332, -5.637186332}
Solution
t = {54.637186332, -5.637186332}

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