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Simplifying 36x9 + 96x5 + 10x = 0 Reorder the terms: 10x + 96x5 + 36x9 = 0 Solving 10x + 96x5 + 36x9 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 48x4 + 18x8) = 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 '(5 + 48x4 + 18x8)' equal to zero and attempt to solve: Simplifying 5 + 48x4 + 18x8 = 0 Solving 5 + 48x4 + 18x8 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + 2.666666667x4 + x8 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + 2.666666667x4 + -0.2777777778 + x8 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + 2.666666667x4 + x8 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + 2.666666667x4 + x8 = 0 + -0.2777777778 2.666666667x4 + x8 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 2.666666667x4 + x8 = -0.2777777778 The x term is 2.666666667x4. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x4 + 1.777777780 + x8 = -0.2777777778 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x4 + x8 = -0.2777777778 + 1.777777780 Combine like terms: -0.2777777778 + 1.777777780 = 1.5000000022 1.777777780 + 2.666666667x4 + x8 = 1.5000000022 Factor a perfect square on the left side: (x4 + 1.333333334)(x4 + 1.333333334) = 1.5000000022 Calculate the square root of the right side: 1.224744872 Break this problem into two subproblems by setting (x4 + 1.333333334) equal to 1.224744872 and -1.224744872.Subproblem 1
x4 + 1.333333334 = 1.224744872 Simplifying x4 + 1.333333334 = 1.224744872 Reorder the terms: 1.333333334 + x4 = 1.224744872 Solving 1.333333334 + x4 = 1.224744872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x4 = 1.224744872 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x4 = 1.224744872 + -1.333333334 x4 = 1.224744872 + -1.333333334 Combine like terms: 1.224744872 + -1.333333334 = -0.108588462 x4 = -0.108588462 Simplifying x4 = -0.108588462 Reorder the terms: 0.108588462 + x4 = -0.108588462 + 0.108588462 Combine like terms: -0.108588462 + 0.108588462 = 0.000000000 0.108588462 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + 1.333333334 = -1.224744872 Simplifying x4 + 1.333333334 = -1.224744872 Reorder the terms: 1.333333334 + x4 = -1.224744872 Solving 1.333333334 + x4 = -1.224744872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x4 = -1.224744872 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x4 = -1.224744872 + -1.333333334 x4 = -1.224744872 + -1.333333334 Combine like terms: -1.224744872 + -1.333333334 = -2.558078206 x4 = -2.558078206 Simplifying x4 = -2.558078206 Reorder the terms: 2.558078206 + x4 = -2.558078206 + 2.558078206 Combine like terms: -2.558078206 + 2.558078206 = 0.000000000 2.558078206 + x4 = 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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