(x^5)+24x=11x^3

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Solution for (x^5)+24x=11x^3 equation:


Simplifying
(x5) + 24x = 11x3
x5 + 24x = 11x3

Reorder the terms:
24x + x5 = 11x3

Solving
24x + x5 = 11x3

Solving for variable 'x'.

Reorder the terms:
24x + -11x3 + x5 = 11x3 + -11x3

Combine like terms: 11x3 + -11x3 = 0
24x + -11x3 + x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(24 + -11x2 + x4) = 0

Factor a trinomial.
x((3 + -1x2)(8 + -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}

Subproblem 3

Set the factor '(8 + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -1x2 = 0 Solving 8 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x2 = 0 + -8 -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1x2 = -8 Divide each side by '-1'. x2 = 8 Simplifying x2 = 8 Take the square root of each side: x = {-2.828427125, 2.828427125}

Solution

x = {0, -1.732050808, 1.732050808, -2.828427125, 2.828427125}

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