T^4+29T^2=100

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Solution for T^4+29T^2=100 equation: 


Simplifying
T4 + 29T2 = 100

Reorder the terms:
29T2 + T4 = 100

Solving
29T2 + T4 = 100

Solving for variable 'T'.

Reorder the terms:
-100 + 29T2 + T4 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 29T2 + T4 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 29T2 + 100 + T4 = 0 + 100

Reorder the terms:
-100 + 100 + 29T2 + T4 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 29T2 + T4 = 0 + 100
29T2 + T4 = 0 + 100

Combine like terms: 0 + 100 = 100
29T2 + T4 = 100

The T term is 29T2.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29T2 + 210.25 + T4 = 100 + 210.25

Reorder the terms:
210.25 + 29T2 + T4 = 100 + 210.25

Combine like terms: 100 + 210.25 = 310.25
210.25 + 29T2 + T4 = 310.25

Factor a perfect square on the left side:
(T2 + 14.5)(T2 + 14.5) = 310.25

Calculate the square root of the right side: 17.613914954

Break this problem into two subproblems by setting 
(T2 + 14.5) equal to 17.613914954 and -17.613914954.


Subproblem 1
T2 + 14.5 = 17.613914954

Simplifying
T2 + 14.5 = 17.613914954

Reorder the terms:
14.5 + T2 = 17.613914954

Solving
14.5 + T2 = 17.613914954

Solving for variable 'T'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + T2 = 17.613914954 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + T2 = 17.613914954 + -14.5
T2 = 17.613914954 + -14.5

Combine like terms: 17.613914954 + -14.5 = 3.113914954
T2 = 3.113914954

Simplifying
T2 = 3.113914954

Take the square root of each side:
T = {-1.764628843, 1.764628843}


Subproblem 2
T2 + 14.5 = -17.613914954

Simplifying
T2 + 14.5 = -17.613914954

Reorder the terms:
14.5 + T2 = -17.613914954

Solving
14.5 + T2 = -17.613914954

Solving for variable 'T'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + T2 = -17.613914954 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + T2 = -17.613914954 + -14.5
T2 = -17.613914954 + -14.5

Combine like terms: -17.613914954 + -14.5 = -32.113914954
T2 = -32.113914954

Simplifying
T2 = -32.113914954

Reorder the terms:
32.113914954 + T2 = -32.113914954 + 32.113914954

Combine like terms: -32.113914954 + 32.113914954 = 0.000000000
32.113914954 + T2 = 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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