t^4+18t^2=81

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Solution for t^4+18t^2=81 equation: 


Simplifying
t4 + 18t2 = 81

Reorder the terms:
18t2 + t4 = 81

Solving
18t2 + t4 = 81

Solving for variable 't'.

Reorder the terms:
-81 + 18t2 + t4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + 18t2 + t4 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 18t2 + 81 + t4 = 0 + 81

Reorder the terms:
-81 + 81 + 18t2 + t4 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 18t2 + t4 = 0 + 81
18t2 + t4 = 0 + 81

Combine like terms: 0 + 81 = 81
18t2 + t4 = 81

The t term is 18t2.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18t2 + 81 + t4 = 81 + 81

Reorder the terms:
81 + 18t2 + t4 = 81 + 81

Combine like terms: 81 + 81 = 162
81 + 18t2 + t4 = 162

Factor a perfect square on the left side:
(t2 + 9)(t2 + 9) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(t2 + 9) equal to 12.727922061 and -12.727922061.


Subproblem 1
t2 + 9 = 12.727922061

Simplifying
t2 + 9 = 12.727922061

Reorder the terms:
9 + t2 = 12.727922061

Solving
9 + t2 = 12.727922061

Solving for variable 't'.

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

Add '-9' to each side of the equation.
9 + -9 + t2 = 12.727922061 + -9

Combine like terms: 9 + -9 = 0
0 + t2 = 12.727922061 + -9
t2 = 12.727922061 + -9

Combine like terms: 12.727922061 + -9 = 3.727922061
t2 = 3.727922061

Simplifying
t2 = 3.727922061

Take the square root of each side:
t = {-1.930782759, 1.930782759}


Subproblem 2
t2 + 9 = -12.727922061

Simplifying
t2 + 9 = -12.727922061

Reorder the terms:
9 + t2 = -12.727922061

Solving
9 + t2 = -12.727922061

Solving for variable 't'.

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

Add '-9' to each side of the equation.
9 + -9 + t2 = -12.727922061 + -9

Combine like terms: 9 + -9 = 0
0 + t2 = -12.727922061 + -9
t2 = -12.727922061 + -9

Combine like terms: -12.727922061 + -9 = -21.727922061
t2 = -21.727922061

Simplifying
t2 = -21.727922061

Reorder the terms:
21.727922061 + t2 = -21.727922061 + 21.727922061

Combine like terms: -21.727922061 + 21.727922061 = 0.000000000
21.727922061 + 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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