0=x^3-5x

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Solution for 0=x^3-5x equation:


Simplifying
0 = x3 + -5x

Reorder the terms:
0 = -5x + x3

Solving
0 = -5x + x3

Solving for variable 'x'.
Remove the zero:
5x + -1x3 = -5x + x3 + 5x + -1x3

Reorder the terms:
5x + -1x3 = -5x + 5x + x3 + -1x3

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -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 '(5 + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -1x2 = 0 Solving 5 + -1x2 = 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 + -1x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x2 = 0 + -5 -1x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1x2 = -5 Divide each side by '-1'. 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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