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Simplifying 6x5 + -8x3 + -6x = 0 Reorder the terms: -6x + -8x3 + 6x5 = 0 Solving -6x + -8x3 + 6x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + -4x2 + 3x4) = 0 Ignore the factor 2.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 = 0Subproblem 2
Set the factor '(-3 + -4x2 + 3x4)' equal to zero and attempt to solve: Simplifying -3 + -4x2 + 3x4 = 0 Solving -3 + -4x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -1.333333333x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.333333333x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -1.333333333x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.333333333x2 + x4 = 0 + 1 -1.333333333x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.333333333x2 + x4 = 1 The x term is -1.333333333x2. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x2 + 0.4444444442 + x4 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x2 + x4 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + -1.333333333x2 + x4 = 1.4444444442 Factor a perfect square on the left side: (x2 + -0.6666666665)(x2 + -0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x2 + -0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
x2 + -0.6666666665 = 1.201850425 Simplifying x2 + -0.6666666665 = 1.201850425 Reorder the terms: -0.6666666665 + x2 = 1.201850425 Solving -0.6666666665 + x2 = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x2 = 1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x2 = 1.201850425 + 0.6666666665 x2 = 1.201850425 + 0.6666666665 Combine like terms: 1.201850425 + 0.6666666665 = 1.8685170915 x2 = 1.8685170915 Simplifying x2 = 1.8685170915 Take the square root of each side: x = {-1.366937121, 1.366937121}Subproblem 2
x2 + -0.6666666665 = -1.201850425 Simplifying x2 + -0.6666666665 = -1.201850425 Reorder the terms: -0.6666666665 + x2 = -1.201850425 Solving -0.6666666665 + x2 = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x2 = -1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x2 = -1.201850425 + 0.6666666665 x2 = -1.201850425 + 0.6666666665 Combine like terms: -1.201850425 + 0.6666666665 = -0.5351837585 x2 = -0.5351837585 Simplifying x2 = -0.5351837585 Reorder the terms: 0.5351837585 + x2 = -0.5351837585 + 0.5351837585 Combine like terms: -0.5351837585 + 0.5351837585 = 0.0000000000 0.5351837585 + x2 = 0.0000000000 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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