x^4+9x^2-1=0

Solution for x^4+9x^2-1=0 equation:

Simplifying
x4 + 9x2 + -1 = 0

Reorder the terms:
-1 + 9x2 + x4 = 0

Solving
-1 + 9x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 9x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + 9x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9x2 + x4 = 0 + 1
9x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
9x2 + x4 = 1

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 = 1 + 20.25

Reorder the terms:
20.25 + 9x2 + x4 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + 9x2 + x4 = 21.25

Factor a perfect square on the left side:
(x2 + 4.5)(x2 + 4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x2 + 4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x2 + 4.5 = 4.609772229

Simplifying
x2 + 4.5 = 4.609772229

Reorder the terms:
4.5 + x2 = 4.609772229

Solving
4.5 + x2 = 4.609772229

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 = 4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x2 = 4.609772229 + -4.5
x2 = 4.609772229 + -4.5

Combine like terms: 4.609772229 + -4.5 = 0.109772229
x2 = 0.109772229

Simplifying
x2 = 0.109772229

Take the square root of each side:
x = {-0.331318923, 0.331318923}

Subproblem 2
x2 + 4.5 = -4.609772229

Simplifying
x2 + 4.5 = -4.609772229

Reorder the terms:
4.5 + x2 = -4.609772229

Solving
4.5 + x2 = -4.609772229

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 = -4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x2 = -4.609772229 + -4.5
x2 = -4.609772229 + -4.5

Combine like terms: -4.609772229 + -4.5 = -9.109772229
x2 = -9.109772229

Simplifying
x2 = -9.109772229

Reorder the terms:
9.109772229 + x2 = -9.109772229 + 9.109772229

Combine like terms: -9.109772229 + 9.109772229 = 0.000000000
9.109772229 + 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.