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Simplifying 20x6 + 4x4 + -10x2 = 0 Reorder the terms: -10x2 + 4x4 + 20x6 = 0 Solving -10x2 + 4x4 + 20x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-5 + 2x2 + 10x4) = 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 '(-5 + 2x2 + 10x4)' equal to zero and attempt to solve: Simplifying -5 + 2x2 + 10x4 = 0 Solving -5 + 2x2 + 10x4 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 0.2x2 + x4 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.2x2 + 0.5 + x4 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.2x2 + x4 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.2x2 + x4 = 0.0 + 0.5 0.2x2 + x4 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.2x2 + x4 = 0.5 The x term is 0.2x2. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x2 + 0.01 + x4 = 0.5 + 0.01 Reorder the terms: 0.01 + 0.2x2 + x4 = 0.5 + 0.01 Combine like terms: 0.5 + 0.01 = 0.51 0.01 + 0.2x2 + x4 = 0.51 Factor a perfect square on the left side: (x2 + 0.1)(x2 + 0.1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (x2 + 0.1) equal to 0.714142843 and -0.714142843.Subproblem 1
x2 + 0.1 = 0.714142843 Simplifying x2 + 0.1 = 0.714142843 Reorder the terms: 0.1 + x2 = 0.714142843 Solving 0.1 + x2 = 0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x2 = 0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x2 = 0.714142843 + -0.1 x2 = 0.714142843 + -0.1 Combine like terms: 0.714142843 + -0.1 = 0.614142843 x2 = 0.614142843 Simplifying x2 = 0.614142843 Take the square root of each side: x = {-0.783672663, 0.783672663}Subproblem 2
x2 + 0.1 = -0.714142843 Simplifying x2 + 0.1 = -0.714142843 Reorder the terms: 0.1 + x2 = -0.714142843 Solving 0.1 + x2 = -0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x2 = -0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x2 = -0.714142843 + -0.1 x2 = -0.714142843 + -0.1 Combine like terms: -0.714142843 + -0.1 = -0.814142843 x2 = -0.814142843 Simplifying x2 = -0.814142843 Reorder the terms: 0.814142843 + x2 = -0.814142843 + 0.814142843 Combine like terms: -0.814142843 + 0.814142843 = 0.000000000 0.814142843 + 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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