X^6-2x^2+1=0

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Solution for X^6-2x^2+1=0 equation:


Simplifying
X6 + -2x2 + 1 = 0

Reorder the terms:
1 + X6 + -2x2 = 0

Solving
1 + X6 + -2x2 = 0

Solving for variable 'X'.

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

Add '-1' to each side of the equation.
1 + X6 + -1 + -2x2 = 0 + -1

Reorder the terms:
1 + -1 + X6 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + X6 + -2x2 = 0 + -1
X6 + -2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
X6 + -2x2 = -1

Add '2x2' to each side of the equation.
X6 + -2x2 + 2x2 = -1 + 2x2

Combine like terms: -2x2 + 2x2 = 0
X6 + 0 = -1 + 2x2
X6 = -1 + 2x2

Simplifying
X6 = -1 + 2x2

Reorder the terms:
1 + X6 + -2x2 = -1 + 2x2 + 1 + -2x2

Reorder the terms:
1 + X6 + -2x2 = -1 + 1 + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
1 + X6 + -2x2 = 0 + 2x2 + -2x2
1 + X6 + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + X6 + -2x2 = 0

Factor a trinomial.
(X3 + -1x)(X3 + 2x) = 0

Subproblem 1

Set the factor '(X3 + -1x)' equal to zero and attempt to solve: Simplifying X3 + -1x = 0 Solving X3 + -1x = 0 Move all terms containing X to the left, all other terms to the right. Add 'x' to each side of the equation. X3 + -1x + x = 0 + x Combine like terms: -1x + x = 0 X3 + 0 = 0 + x X3 = 0 + x Remove the zero: X3 = x Simplifying X3 = x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(X3 + 2x)' equal to zero and attempt to solve: Simplifying X3 + 2x = 0 Solving X3 + 2x = 0 Move all terms containing X to the left, all other terms to the right. Add '-2x' to each side of the equation. X3 + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 X3 + 0 = 0 + -2x X3 = 0 + -2x Remove the zero: X3 = -2x Simplifying X3 = -2x 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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