x^4+11x^2-44=0

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Solution for x^4+11x^2-44=0 equation: 


Simplifying
x4 + 11x2 + -44 = 0

Reorder the terms:
-44 + 11x2 + x4 = 0

Solving
-44 + 11x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 11x2 + 44 + x4 = 0 + 44

Reorder the terms:
-44 + 44 + 11x2 + x4 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 11x2 + x4 = 0 + 44
11x2 + x4 = 0 + 44

Combine like terms: 0 + 44 = 44
11x2 + x4 = 44

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 = 44 + 30.25

Reorder the terms:
30.25 + 11x2 + x4 = 44 + 30.25

Combine like terms: 44 + 30.25 = 74.25
30.25 + 11x2 + x4 = 74.25

Factor a perfect square on the left side:
(x2 + 5.5)(x2 + 5.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x2 + 5.5) equal to 8.61684397 and -8.61684397.


Subproblem 1
x2 + 5.5 = 8.61684397

Simplifying
x2 + 5.5 = 8.61684397

Reorder the terms:
5.5 + x2 = 8.61684397

Solving
5.5 + x2 = 8.61684397

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 = 8.61684397 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = 8.61684397 + -5.5
x2 = 8.61684397 + -5.5

Combine like terms: 8.61684397 + -5.5 = 3.11684397
x2 = 3.11684397

Simplifying
x2 = 3.11684397

Take the square root of each side:
x = {-1.765458572, 1.765458572}


Subproblem 2
x2 + 5.5 = -8.61684397

Simplifying
x2 + 5.5 = -8.61684397

Reorder the terms:
5.5 + x2 = -8.61684397

Solving
5.5 + x2 = -8.61684397

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 = -8.61684397 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = -8.61684397 + -5.5
x2 = -8.61684397 + -5.5

Combine like terms: -8.61684397 + -5.5 = -14.11684397
x2 = -14.11684397

Simplifying
x2 = -14.11684397

Reorder the terms:
14.11684397 + x2 = -14.11684397 + 14.11684397

Combine like terms: -14.11684397 + 14.11684397 = 0.00000000
14.11684397 + x2 = 0.00000000

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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