x^3-4x=x

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Solution for x^3-4x=x equation:


Simplifying
x3 + -4x = x

Reorder the terms:
-4x + x3 = x

Solving
-4x + x3 = x

Solving for variable 'x'.

Reorder the terms:
-4x + -1x + x3 = x + -1x

Combine like terms: -4x + -1x = -5x
-5x + x3 = x + -1x

Combine like terms: x + -1x = 0
-5x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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}

Solution

x = {0, -2.236067978, 2.236067978}

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