4x^4-36x^2-81=0

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Solution for 4x^4-36x^2-81=0 equation: 


Simplifying
4x4 + -36x2 + -81 = 0

Reorder the terms:
-81 + -36x2 + 4x4 = 0

Solving
-81 + -36x2 + 4x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-20.25 + -9x2 + x4 = 0

Move the constant term to the right:

Add '20.25' to each side of the equation.
-20.25 + -9x2 + 20.25 + x4 = 0 + 20.25

Reorder the terms:
-20.25 + 20.25 + -9x2 + x4 = 0 + 20.25

Combine like terms: -20.25 + 20.25 = 0.00
0.00 + -9x2 + x4 = 0 + 20.25
-9x2 + x4 = 0 + 20.25

Combine like terms: 0 + 20.25 = 20.25
-9x2 + x4 = 20.25

The x term is -9x2.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x2 + 20.25 + x4 = 20.25 + 20.25

Reorder the terms:
20.25 + -9x2 + x4 = 20.25 + 20.25

Combine like terms: 20.25 + 20.25 = 40.5
20.25 + -9x2 + x4 = 40.5

Factor a perfect square on the left side:
(x2 + -4.5)(x2 + -4.5) = 40.5

Calculate the square root of the right side: 6.363961031

Break this problem into two subproblems by setting 
(x2 + -4.5) equal to 6.363961031 and -6.363961031.


Subproblem 1
x2 + -4.5 = 6.363961031

Simplifying
x2 + -4.5 = 6.363961031

Reorder the terms:
-4.5 + x2 = 6.363961031

Solving
-4.5 + x2 = 6.363961031

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x2 = 6.363961031 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x2 = 6.363961031 + 4.5
x2 = 6.363961031 + 4.5

Combine like terms: 6.363961031 + 4.5 = 10.863961031
x2 = 10.863961031

Simplifying
x2 = 10.863961031

Take the square root of each side:
x = {-3.29605234, 3.29605234}


Subproblem 2
x2 + -4.5 = -6.363961031

Simplifying
x2 + -4.5 = -6.363961031

Reorder the terms:
-4.5 + x2 = -6.363961031

Solving
-4.5 + x2 = -6.363961031

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x2 = -6.363961031 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x2 = -6.363961031 + 4.5
x2 = -6.363961031 + 4.5

Combine like terms: -6.363961031 + 4.5 = -1.863961031
x2 = -1.863961031

Simplifying
x2 = -1.863961031

Reorder the terms:
1.863961031 + x2 = -1.863961031 + 1.863961031

Combine like terms: -1.863961031 + 1.863961031 = 0.000000000
1.863961031 + x2 = 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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