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Simplifying 2x9 + -24x5 + 6x = 0 Reorder the terms: 6x + -24x5 + 2x9 = 0 Solving 6x + -24x5 + 2x9 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -12x4 + x8) = 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 + -12x4 + x8)' equal to zero and attempt to solve: Simplifying 3 + -12x4 + x8 = 0 Solving 3 + -12x4 + x8 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -12x4 + -3 + x8 = 0 + -3 Reorder the terms: 3 + -3 + -12x4 + x8 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12x4 + x8 = 0 + -3 -12x4 + x8 = 0 + -3 Combine like terms: 0 + -3 = -3 -12x4 + x8 = -3 The x term is -12x4. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x4 + 36 + x8 = -3 + 36 Reorder the terms: 36 + -12x4 + x8 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + -12x4 + x8 = 33 Factor a perfect square on the left side: (x4 + -6)(x4 + -6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x4 + -6) equal to 5.744562647 and -5.744562647.Subproblem 1
x4 + -6 = 5.744562647 Simplifying x4 + -6 = 5.744562647 Reorder the terms: -6 + x4 = 5.744562647 Solving -6 + x4 = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x4 = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x4 = 5.744562647 + 6 x4 = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 x4 = 11.744562647 Simplifying x4 = 11.744562647 Reorder the terms: -11.744562647 + x4 = 11.744562647 + -11.744562647 Combine like terms: 11.744562647 + -11.744562647 = 0.000000000 -11.744562647 + 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 + -6 = -5.744562647 Simplifying x4 + -6 = -5.744562647 Reorder the terms: -6 + x4 = -5.744562647 Solving -6 + x4 = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x4 = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x4 = -5.744562647 + 6 x4 = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 x4 = 0.255437353 Simplifying x4 = 0.255437353 Reorder the terms: -0.255437353 + x4 = 0.255437353 + -0.255437353 Combine like terms: 0.255437353 + -0.255437353 = 0.000000000 -0.255437353 + 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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