0=x^3-13x

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Solution for 0=x^3-13x equation:


Simplifying
0 = x3 + -13x

Reorder the terms:
0 = -13x + x3

Solving
0 = -13x + x3

Solving for variable 'x'.
Remove the zero:
13x + -1x3 = -13x + x3 + 13x + -1x3

Reorder the terms:
13x + -1x3 = -13x + 13x + x3 + -1x3

Combine like terms: -13x + 13x = 0
13x + -1x3 = 0 + x3 + -1x3
13x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
13x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -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 '(13 + -1x2)' equal to zero and attempt to solve: Simplifying 13 + -1x2 = 0 Solving 13 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x2 = 0 + -13 -1x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -1x2 = -13 Divide each side by '-1'. x2 = 13 Simplifying x2 = 13 Take the square root of each side: x = {-3.605551275, 3.605551275}

Solution

x = {0, -3.605551275, 3.605551275}

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