0=x^3-3x

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


Simplifying
0 = x3 + -3x

Reorder the terms:
0 = -3x + x3

Solving
0 = -3x + x3

Solving for variable 'x'.
Remove the zero:
3x + -1x3 = -3x + x3 + 3x + -1x3

Reorder the terms:
3x + -1x3 = -3x + 3x + x3 + -1x3

Combine like terms: -3x + 3x = 0
3x + -1x3 = 0 + x3 + -1x3
3x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
3x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -1x2) = 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 '(3 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}

Solution

x = {0, -1.732050808, 1.732050808}

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