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Simplifying x7 + 5x4 + -40x = 0 Reorder the terms: -40x + 5x4 + x7 = 0 Solving -40x + 5x4 + x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + 5x3 + x6) = 0Subproblem 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 '(-40 + 5x3 + x6)' equal to zero and attempt to solve: Simplifying -40 + 5x3 + x6 = 0 Solving -40 + 5x3 + x6 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 5x3 + 40 + x6 = 0 + 40 Reorder the terms: -40 + 40 + 5x3 + x6 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 5x3 + x6 = 0 + 40 5x3 + x6 = 0 + 40 Combine like terms: 0 + 40 = 40 5x3 + x6 = 40 The x term is 5x3. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x3 + 6.25 + x6 = 40 + 6.25 Reorder the terms: 6.25 + 5x3 + x6 = 40 + 6.25 Combine like terms: 40 + 6.25 = 46.25 6.25 + 5x3 + x6 = 46.25 Factor a perfect square on the left side: (x3 + 2.5)(x3 + 2.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x3 + 2.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x3 + 2.5 = 6.800735254 Simplifying x3 + 2.5 = 6.800735254 Reorder the terms: 2.5 + x3 = 6.800735254 Solving 2.5 + x3 = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x3 = 6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x3 = 6.800735254 + -2.5 x3 = 6.800735254 + -2.5 Combine like terms: 6.800735254 + -2.5 = 4.300735254 x3 = 4.300735254 Simplifying x3 = 4.300735254 Reorder the terms: -4.300735254 + x3 = 4.300735254 + -4.300735254 Combine like terms: 4.300735254 + -4.300735254 = 0.000000000 -4.300735254 + x3 = 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
x3 + 2.5 = -6.800735254 Simplifying x3 + 2.5 = -6.800735254 Reorder the terms: 2.5 + x3 = -6.800735254 Solving 2.5 + x3 = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x3 = -6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x3 = -6.800735254 + -2.5 x3 = -6.800735254 + -2.5 Combine like terms: -6.800735254 + -2.5 = -9.300735254 x3 = -9.300735254 Simplifying x3 = -9.300735254 Reorder the terms: 9.300735254 + x3 = -9.300735254 + 9.300735254 Combine like terms: -9.300735254 + 9.300735254 = 0.000000000 9.300735254 + x3 = 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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