27x^5-75x=0

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Solution for 27x^5-75x=0 equation:


Simplifying
27x5 + -75x = 0

Reorder the terms:
-75x + 27x5 = 0

Solving
-75x + 27x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-25 + 9x4) = 0

Factor a difference between two squares.
3x((5 + 3x2)(-5 + 3x2)) = 0

Ignore the factor 3.

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 + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 3x2 = 0 Solving 5 + 3x2 = 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 + 3x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x2 = 0 + -5 3x2 = 0 + -5 Combine like terms: 0 + -5 = -5 3x2 = -5 Divide each side by '3'. x2 = -1.666666667 Simplifying x2 = -1.666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(-5 + 3x2)' equal to zero and attempt to solve: Simplifying -5 + 3x2 = 0 Solving -5 + 3x2 = 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 + 3x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x2 = 0 + 5 3x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3x2 = 5 Divide each side by '3'. x2 = 1.666666667 Simplifying x2 = 1.666666667 Take the square root of each side: x = {-1.290994449, 1.290994449}

Solution

x = {0, -1.290994449, 1.290994449}

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