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Simplifying X5 + 5X3 + -3X = 0 Reorder the terms: -3X + 5X3 + X5 = 0 Solving -3X + 5X3 + X5 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(-3 + 5X2 + 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 '(-3 + 5X2 + X4)' equal to zero and attempt to solve: Simplifying -3 + 5X2 + X4 = 0 Solving -3 + 5X2 + X4 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 5X2 + 3 + X4 = 0 + 3 Reorder the terms: -3 + 3 + 5X2 + X4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5X2 + X4 = 0 + 3 5X2 + X4 = 0 + 3 Combine like terms: 0 + 3 = 3 5X2 + X4 = 3 The X term is 5X2. 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. 5X2 + 6.25 + X4 = 3 + 6.25 Reorder the terms: 6.25 + 5X2 + X4 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + 5X2 + X4 = 9.25 Factor a perfect square on the left side: (X2 + 2.5)(X2 + 2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (X2 + 2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
X2 + 2.5 = 3.041381265 Simplifying X2 + 2.5 = 3.041381265 Reorder the terms: 2.5 + X2 = 3.041381265 Solving 2.5 + X2 = 3.041381265 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 + X2 = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X2 = 3.041381265 + -2.5 X2 = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 X2 = 0.541381265 Simplifying X2 = 0.541381265 Take the square root of each side: X = {-0.735786154, 0.735786154}Subproblem 2
X2 + 2.5 = -3.041381265 Simplifying X2 + 2.5 = -3.041381265 Reorder the terms: 2.5 + X2 = -3.041381265 Solving 2.5 + X2 = -3.041381265 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 + X2 = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X2 = -3.041381265 + -2.5 X2 = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 X2 = -5.541381265 Simplifying X2 = -5.541381265 Reorder the terms: 5.541381265 + X2 = -5.541381265 + 5.541381265 Combine like terms: -5.541381265 + 5.541381265 = 0.000000000 5.541381265 + 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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