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Simplifying X5 + -8X3 + -9X = X Reorder the terms: -9X + -8X3 + X5 = X Solving -9X + -8X3 + X5 = X Solving for variable 'X'. Reorder the terms: -9X + -1X + -8X3 + X5 = X + -1X Combine like terms: -9X + -1X = -10X -10X + -8X3 + X5 = X + -1X Combine like terms: X + -1X = 0 -10X + -8X3 + X5 = 0 Factor out the Greatest Common Factor (GCF), 'X'. X(-10 + -8X2 + 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 '(-10 + -8X2 + X4)' equal to zero and attempt to solve: Simplifying -10 + -8X2 + X4 = 0 Solving -10 + -8X2 + X4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -8X2 + 10 + X4 = 0 + 10 Reorder the terms: -10 + 10 + -8X2 + X4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8X2 + X4 = 0 + 10 -8X2 + X4 = 0 + 10 Combine like terms: 0 + 10 = 10 -8X2 + X4 = 10 The X term is -8X2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X2 + 16 + X4 = 10 + 16 Reorder the terms: 16 + -8X2 + X4 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8X2 + X4 = 26 Factor a perfect square on the left side: (X2 + -4)(X2 + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (X2 + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
X2 + -4 = 5.099019514 Simplifying X2 + -4 = 5.099019514 Reorder the terms: -4 + X2 = 5.099019514 Solving -4 + X2 = 5.099019514 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X2 = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + X2 = 5.099019514 + 4 X2 = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 X2 = 9.099019514 Simplifying X2 = 9.099019514 Take the square root of each side: X = {-3.016458107, 3.016458107}Subproblem 2
X2 + -4 = -5.099019514 Simplifying X2 + -4 = -5.099019514 Reorder the terms: -4 + X2 = -5.099019514 Solving -4 + X2 = -5.099019514 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X2 = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + X2 = -5.099019514 + 4 X2 = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 X2 = -1.099019514 Simplifying X2 = -1.099019514 Reorder the terms: 1.099019514 + X2 = -1.099019514 + 1.099019514 Combine like terms: -1.099019514 + 1.099019514 = 0.000000000 1.099019514 + 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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