5x^6-10x^2+20x^4=0

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Solution for 5x^6-10x^2+20x^4=0 equation:


Simplifying
5x6 + -10x2 + 20x4 = 0

Reorder the terms:
-10x2 + 20x4 + 5x6 = 0

Solving
-10x2 + 20x4 + 5x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-2 + 4x2 + x4) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(-2 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + 4x2 + x4 = 0 Solving -2 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 4x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x2 + x4 = 0 + 2 4x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 4x2 + x4 = 2 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 2 + 4 Reorder the terms: 4 + 4x2 + x4 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4x2 + x4 = 6 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + 2) equal to 2.449489743 and -2.449489743.

Subproblem 1

x2 + 2 = 2.449489743 Simplifying x2 + 2 = 2.449489743 Reorder the terms: 2 + x2 = 2.449489743 Solving 2 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.449489743 + -2 x2 = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 x2 = 0.449489743 Simplifying x2 = 0.449489743 Take the square root of each side: x = {-0.670439962, 0.670439962}

Subproblem 2

x2 + 2 = -2.449489743 Simplifying x2 + 2 = -2.449489743 Reorder the terms: 2 + x2 = -2.449489743 Solving 2 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.449489743 + -2 x2 = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 x2 = -4.449489743 Simplifying x2 = -4.449489743 Reorder the terms: 4.449489743 + x2 = -4.449489743 + 4.449489743 Combine like terms: -4.449489743 + 4.449489743 = 0.000000000 4.449489743 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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