x^4-6x^2+9=1

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Solution for x^4-6x^2+9=1 equation: 


Simplifying
x4 + -6x2 + 9 = 1

Reorder the terms:
9 + -6x2 + x4 = 1

Solving
9 + -6x2 + x4 = 1

Solving for variable 'x'.

Reorder the terms:
9 + -1 + -6x2 + x4 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -6x2 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -6x2 + x4 = 0

Factor a trinomial.
(2 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(2 + -1x2)((2 + x)(2 + -1x)) = 0


Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.414213562, 1.414213562, -2, 2}

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