x^5-10x^3+10x=0

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Solution for x^5-10x^3+10x=0 equation:


Simplifying
x5 + -10x3 + 10x = 0

Reorder the terms:
10x + -10x3 + x5 = 0

Solving
10x + -10x3 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -10x2 + x4) = 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 '(10 + -10x2 + x4)' equal to zero and attempt to solve: Simplifying 10 + -10x2 + x4 = 0 Solving 10 + -10x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10x2 + -10 + x4 = 0 + -10 Reorder the terms: 10 + -10 + -10x2 + x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10x2 + x4 = 0 + -10 -10x2 + x4 = 0 + -10 Combine like terms: 0 + -10 = -10 -10x2 + x4 = -10 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = -10 + 25 Reorder the terms: 25 + -10x2 + x4 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + -10x2 + x4 = 15 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + -5) equal to 3.872983346 and -3.872983346.

Subproblem 1

x2 + -5 = 3.872983346 Simplifying x2 + -5 = 3.872983346 Reorder the terms: -5 + x2 = 3.872983346 Solving -5 + x2 = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 3.872983346 + 5 x2 = 3.872983346 + 5 Combine like terms: 3.872983346 + 5 = 8.872983346 x2 = 8.872983346 Simplifying x2 = 8.872983346 Take the square root of each side: x = {-2.978755335, 2.978755335}

Subproblem 2

x2 + -5 = -3.872983346 Simplifying x2 + -5 = -3.872983346 Reorder the terms: -5 + x2 = -3.872983346 Solving -5 + x2 = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -3.872983346 + 5 x2 = -3.872983346 + 5 Combine like terms: -3.872983346 + 5 = 1.127016654 x2 = 1.127016654 Simplifying x2 = 1.127016654 Take the square root of each side: x = {-1.061610406, 1.061610406}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.978755335, 2.978755335, -1.061610406, 1.061610406}

Solution

x = {0, -2.978755335, 2.978755335, -1.061610406, 1.061610406}

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