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Simplifying 12x6 + -8x4 + -16x2 = 0 Reorder the terms: -16x2 + -8x4 + 12x6 = 0 Solving -16x2 + -8x4 + 12x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-4 + -2x2 + 3x4) = 0 Ignore the factor 4.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 '(-4 + -2x2 + 3x4)' equal to zero and attempt to solve: Simplifying -4 + -2x2 + 3x4 = 0 Solving -4 + -2x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -0.6666666667x2 + x4 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.6666666667x2 + 1.333333333 + x4 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.6666666667x2 + x4 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.6666666667x2 + x4 = 0 + 1.333333333 -0.6666666667x2 + x4 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.6666666667x2 + x4 = 1.333333333 The x term is -0.6666666667x2. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x2 + 0.1111111112 + x4 = 1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x2 + x4 = 1.333333333 + 0.1111111112 Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442 0.1111111112 + -0.6666666667x2 + x4 = 1.4444444442 Factor a perfect square on the left side: (x2 + -0.3333333334)(x2 + -0.3333333334) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x2 + -0.3333333334) equal to 1.201850425 and -1.201850425.Subproblem 1
x2 + -0.3333333334 = 1.201850425 Simplifying x2 + -0.3333333334 = 1.201850425 Reorder the terms: -0.3333333334 + x2 = 1.201850425 Solving -0.3333333334 + x2 = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x2 = 1.201850425 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = 1.201850425 + 0.3333333334 x2 = 1.201850425 + 0.3333333334 Combine like terms: 1.201850425 + 0.3333333334 = 1.5351837584 x2 = 1.5351837584 Simplifying x2 = 1.5351837584 Take the square root of each side: x = {-1.239025326, 1.239025326}Subproblem 2
x2 + -0.3333333334 = -1.201850425 Simplifying x2 + -0.3333333334 = -1.201850425 Reorder the terms: -0.3333333334 + x2 = -1.201850425 Solving -0.3333333334 + x2 = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x2 = -1.201850425 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = -1.201850425 + 0.3333333334 x2 = -1.201850425 + 0.3333333334 Combine like terms: -1.201850425 + 0.3333333334 = -0.8685170916 x2 = -0.8685170916 Simplifying x2 = -0.8685170916 Reorder the terms: 0.8685170916 + x2 = -0.8685170916 + 0.8685170916 Combine like terms: -0.8685170916 + 0.8685170916 = 0.0000000000 0.8685170916 + 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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