0=x^4-6x^2+5

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Solution for 0=x^4-6x^2+5 equation: 


Simplifying
0 = x4 + -6x2 + 5

Reorder the terms:
0 = 5 + -6x2 + x4

Solving
0 = 5 + -6x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + 6x2 + -1x4 = 5 + -6x2 + x4 + -5 + 6x2 + -1x4

Reorder the terms:
-5 + 6x2 + -1x4 = 5 + -5 + -6x2 + 6x2 + x4 + -1x4

Combine like terms: 5 + -5 = 0
-5 + 6x2 + -1x4 = 0 + -6x2 + 6x2 + x4 + -1x4
-5 + 6x2 + -1x4 = -6x2 + 6x2 + x4 + -1x4

Combine like terms: -6x2 + 6x2 = 0
-5 + 6x2 + -1x4 = 0 + x4 + -1x4
-5 + 6x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-5 + 6x2 + -1x4 = 0

Factor a trinomial.
(-5 + x2)(1 + -1x2) = 0

Factor a difference between two squares.
(-5 + x2)((1 + x)(1 + -1x)) = 0


Subproblem 1
Set the factor '(-5 + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x2 = 0

Solving
-5 + x2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x2 = 0 + 5
x2 = 0 + 5

Combine like terms: 0 + 5 = 5
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.236067978, 2.236067978, -1, 1}

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