t^6+1t^3=36

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Solution for t^6+1t^3=36 equation: 


Simplifying
t6 + 1t3 = 36

Reorder the terms:
1t3 + t6 = 36

Solving
1t3 + t6 = 36

Solving for variable 't'.

Reorder the terms:
-36 + 1t3 + t6 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 1t3 + t6 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 1t3 + 36 + t6 = 0 + 36

Reorder the terms:
-36 + 36 + 1t3 + t6 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 1t3 + t6 = 0 + 36
1t3 + t6 = 0 + 36

Combine like terms: 0 + 36 = 36
1t3 + t6 = 36

The t term is 1t3.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t3 + 0.25 + t6 = 36 + 0.25

Reorder the terms:
0.25 + t3 + t6 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + t3 + t6 = 36.25

Factor a perfect square on the left side:
(t3 + 0.5)(t3 + 0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(t3 + 0.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
t3 + 0.5 = 6.020797289

Simplifying
t3 + 0.5 = 6.020797289

Reorder the terms:
0.5 + t3 = 6.020797289

Solving
0.5 + t3 = 6.020797289

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t3 = 6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t3 = 6.020797289 + -0.5
t3 = 6.020797289 + -0.5

Combine like terms: 6.020797289 + -0.5 = 5.520797289
t3 = 5.520797289

Simplifying
t3 = 5.520797289

Reorder the terms:
-5.520797289 + t3 = 5.520797289 + -5.520797289

Combine like terms: 5.520797289 + -5.520797289 = 0.000000000
-5.520797289 + t3 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
t3 + 0.5 = -6.020797289

Simplifying
t3 + 0.5 = -6.020797289

Reorder the terms:
0.5 + t3 = -6.020797289

Solving
0.5 + t3 = -6.020797289

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t3 = -6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t3 = -6.020797289 + -0.5
t3 = -6.020797289 + -0.5

Combine like terms: -6.020797289 + -0.5 = -6.520797289
t3 = -6.520797289

Simplifying
t3 = -6.520797289

Reorder the terms:
6.520797289 + t3 = -6.520797289 + 6.520797289

Combine like terms: -6.520797289 + 6.520797289 = 0.000000000
6.520797289 + t3 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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