x^4+11x^2-45=0

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Solution for x^4+11x^2-45=0 equation: 


Simplifying
x4 + 11x2 + -45 = 0

Reorder the terms:
-45 + 11x2 + x4 = 0

Solving
-45 + 11x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 11x2 + 45 + x4 = 0 + 45

Reorder the terms:
-45 + 45 + 11x2 + x4 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 11x2 + x4 = 0 + 45
11x2 + x4 = 0 + 45

Combine like terms: 0 + 45 = 45
11x2 + x4 = 45

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 = 45 + 30.25

Reorder the terms:
30.25 + 11x2 + x4 = 45 + 30.25

Combine like terms: 45 + 30.25 = 75.25
30.25 + 11x2 + x4 = 75.25

Factor a perfect square on the left side:
(x2 + 5.5)(x2 + 5.5) = 75.25

Calculate the square root of the right side: 8.674675786

Break this problem into two subproblems by setting 
(x2 + 5.5) equal to 8.674675786 and -8.674675786.


Subproblem 1
x2 + 5.5 = 8.674675786

Simplifying
x2 + 5.5 = 8.674675786

Reorder the terms:
5.5 + x2 = 8.674675786

Solving
5.5 + x2 = 8.674675786

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 = 8.674675786 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = 8.674675786 + -5.5
x2 = 8.674675786 + -5.5

Combine like terms: 8.674675786 + -5.5 = 3.174675786
x2 = 3.174675786

Simplifying
x2 = 3.174675786

Take the square root of each side:
x = {-1.781761989, 1.781761989}


Subproblem 2
x2 + 5.5 = -8.674675786

Simplifying
x2 + 5.5 = -8.674675786

Reorder the terms:
5.5 + x2 = -8.674675786

Solving
5.5 + x2 = -8.674675786

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 = -8.674675786 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = -8.674675786 + -5.5
x2 = -8.674675786 + -5.5

Combine like terms: -8.674675786 + -5.5 = -14.174675786
x2 = -14.174675786

Simplifying
x2 = -14.174675786

Reorder the terms:
14.174675786 + x2 = -14.174675786 + 14.174675786

Combine like terms: -14.174675786 + 14.174675786 = 0.000000000
14.174675786 + 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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