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Simplifying X5 + -25X3 + -16X = 0 Reorder the terms: -16X + -25X3 + X5 = 0 Solving -16X + -25X3 + X5 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-16 + -25X2 + X4) = 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 '(-16 + -25X2 + X4)' equal to zero and attempt to solve: Simplifying -16 + -25X2 + X4 = 0 Solving -16 + -25X2 + X4 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -25X2 + 16 + X4 = 0 + 16 Reorder the terms: -16 + 16 + -25X2 + X4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -25X2 + X4 = 0 + 16 -25X2 + X4 = 0 + 16 Combine like terms: 0 + 16 = 16 -25X2 + X4 = 16 The X term is -25X2. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25X2 + 156.25 + X4 = 16 + 156.25 Reorder the terms: 156.25 + -25X2 + X4 = 16 + 156.25 Combine like terms: 16 + 156.25 = 172.25 156.25 + -25X2 + X4 = 172.25 Factor a perfect square on the left side: (X2 + -12.5)(X2 + -12.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (X2 + -12.5) equal to 13.124404748 and -13.124404748.Subproblem 1
X2 + -12.5 = 13.124404748 Simplifying X2 + -12.5 = 13.124404748 Reorder the terms: -12.5 + X2 = 13.124404748 Solving -12.5 + X2 = 13.124404748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + X2 = 13.124404748 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + X2 = 13.124404748 + 12.5 X2 = 13.124404748 + 12.5 Combine like terms: 13.124404748 + 12.5 = 25.624404748 X2 = 25.624404748 Simplifying X2 = 25.624404748 Take the square root of each side: X = {-5.062055388, 5.062055388}Subproblem 2
X2 + -12.5 = -13.124404748 Simplifying X2 + -12.5 = -13.124404748 Reorder the terms: -12.5 + X2 = -13.124404748 Solving -12.5 + X2 = -13.124404748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + X2 = -13.124404748 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + X2 = -13.124404748 + 12.5 X2 = -13.124404748 + 12.5 Combine like terms: -13.124404748 + 12.5 = -0.624404748 X2 = -0.624404748 Simplifying X2 = -0.624404748 Reorder the terms: 0.624404748 + X2 = -0.624404748 + 0.624404748 Combine like terms: -0.624404748 + 0.624404748 = 0.000000000 0.624404748 + X2 = 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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