4x^4-44x^2-45=0

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Solution for 4x^4-44x^2-45=0 equation: 


Simplifying
4x4 + -44x2 + -45 = 0

Reorder the terms:
-45 + -44x2 + 4x4 = 0

Solving
-45 + -44x2 + 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'.
-11.25 + -11x2 + x4 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -11x2 + 11.25 + x4 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -11x2 + x4 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -11x2 + x4 = 0 + 11.25
-11x2 + x4 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-11x2 + x4 = 11.25

The x term is -11x2.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x2 + 30.25 + x4 = 11.25 + 30.25

Reorder the terms:
30.25 + -11x2 + x4 = 11.25 + 30.25

Combine like terms: 11.25 + 30.25 = 41.5
30.25 + -11x2 + x4 = 41.5

Factor a perfect square on the left side:
(x2 + -5.5)(x2 + -5.5) = 41.5

Calculate the square root of the right side: 6.442049363

Break this problem into two subproblems by setting 
(x2 + -5.5) equal to 6.442049363 and -6.442049363.


Subproblem 1
x2 + -5.5 = 6.442049363

Simplifying
x2 + -5.5 = 6.442049363

Reorder the terms:
-5.5 + x2 = 6.442049363

Solving
-5.5 + x2 = 6.442049363

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x2 = 6.442049363 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = 6.442049363 + 5.5
x2 = 6.442049363 + 5.5

Combine like terms: 6.442049363 + 5.5 = 11.942049363
x2 = 11.942049363

Simplifying
x2 = 11.942049363

Take the square root of each side:
x = {-3.455727038, 3.455727038}


Subproblem 2
x2 + -5.5 = -6.442049363

Simplifying
x2 + -5.5 = -6.442049363

Reorder the terms:
-5.5 + x2 = -6.442049363

Solving
-5.5 + x2 = -6.442049363

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x2 = -6.442049363 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = -6.442049363 + 5.5
x2 = -6.442049363 + 5.5

Combine like terms: -6.442049363 + 5.5 = -0.942049363
x2 = -0.942049363

Simplifying
x2 = -0.942049363

Reorder the terms:
0.942049363 + x2 = -0.942049363 + 0.942049363

Combine like terms: -0.942049363 + 0.942049363 = 0.000000000
0.942049363 + 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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