8x^6+4x^4-2x^2=

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Solution for 8x^6+4x^4-2x^2= equation:


Simplifying
8x6 + 4x4 + -2x2 = 0

Reorder the terms:
-2x2 + 4x4 + 8x6 = 0

Solving
-2x2 + 4x4 + 8x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-1 + 2x2 + 4x4) = 0

Ignore the factor 2.

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 '(-1 + 2x2 + 4x4)' equal to zero and attempt to solve: Simplifying -1 + 2x2 + 4x4 = 0 Solving -1 + 2x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.5x2 + 0.25 + x4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.5x2 + x4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.5x2 + x4 = 0 + 0.25 0.5x2 + x4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.5x2 + x4 = 0.25 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = 0.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = 0.25 + 0.0625 Combine like terms: 0.25 + 0.0625 = 0.3125 0.0625 + 0.5x2 + x4 = 0.3125 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x2 + 0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1

x2 + 0.25 = 0.559016994 Simplifying x2 + 0.25 = 0.559016994 Reorder the terms: 0.25 + x2 = 0.559016994 Solving 0.25 + x2 = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0.559016994 + -0.25 x2 = 0.559016994 + -0.25 Combine like terms: 0.559016994 + -0.25 = 0.309016994 x2 = 0.309016994 Simplifying x2 = 0.309016994 Take the square root of each side: x = {-0.55589297, 0.55589297}

Subproblem 2

x2 + 0.25 = -0.559016994 Simplifying x2 + 0.25 = -0.559016994 Reorder the terms: 0.25 + x2 = -0.559016994 Solving 0.25 + x2 = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = -0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = -0.559016994 + -0.25 x2 = -0.559016994 + -0.25 Combine like terms: -0.559016994 + -0.25 = -0.809016994 x2 = -0.809016994 Simplifying x2 = -0.809016994 Reorder the terms: 0.809016994 + x2 = -0.809016994 + 0.809016994 Combine like terms: -0.809016994 + 0.809016994 = 0.000000000 0.809016994 + 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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