x^3-0.25x=0

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Solution for x^3-0.25x=0 equation:


Simplifying
x3 + -0.25x = 0

Reorder the terms:
-0.25x + x3 = 0

Solving
-0.25x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-0.25 + x2) = 0

Factor a difference between two squares.
x((0.5 + x)(-0.5 + x)) = 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 '(0.5 + x)' equal to zero and attempt to solve: Simplifying 0.5 + x = 0 Solving 0.5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0 + -0.5 x = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5

Subproblem 3

Set the factor '(-0.5 + x)' equal to zero and attempt to solve: Simplifying -0.5 + x = 0 Solving -0.5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0 + 0.5 x = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

x = {0, -0.5, 0.5}

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