t^4-t^2-1=0

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Solution for t^4-t^2-1=0 equation: 


Simplifying
t4 + -1t2 + -1 = 0

Reorder the terms:
-1 + -1t2 + t4 = 0

Solving
-1 + -1t2 + t4 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1t2 + 1 + t4 = 0 + 1

Reorder the terms:
-1 + 1 + -1t2 + t4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t2 + t4 = 0 + 1
-1t2 + t4 = 0 + 1

Combine like terms: 0 + 1 = 1
-1t2 + t4 = 1

The t term is -1t2.  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.
-1t2 + 0.25 + t4 = 1 + 0.25

Reorder the terms:
0.25 + -1t2 + t4 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1t2 + t4 = 1.25

Factor a perfect square on the left side:
(t2 + -0.5)(t2 + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(t2 + -0.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
t2 + -0.5 = 1.118033989

Simplifying
t2 + -0.5 = 1.118033989

Reorder the terms:
-0.5 + t2 = 1.118033989

Solving
-0.5 + t2 = 1.118033989

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 + t2 = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t2 = 1.118033989 + 0.5
t2 = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
t2 = 1.618033989

Simplifying
t2 = 1.618033989

Take the square root of each side:
t = {-1.27201965, 1.27201965}


Subproblem 2
t2 + -0.5 = -1.118033989

Simplifying
t2 + -0.5 = -1.118033989

Reorder the terms:
-0.5 + t2 = -1.118033989

Solving
-0.5 + t2 = -1.118033989

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 + t2 = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t2 = -1.118033989 + 0.5
t2 = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
t2 = -0.618033989

Simplifying
t2 = -0.618033989

Reorder the terms:
0.618033989 + t2 = -0.618033989 + 0.618033989

Combine like terms: -0.618033989 + 0.618033989 = 0.000000000
0.618033989 + 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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