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Simplifying 2x5 + 32x3 + -944x = 0 Reorder the terms: -944x + 32x3 + 2x5 = 0 Solving -944x + 32x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-472 + 16x2 + x4) = 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 '(-472 + 16x2 + x4)' equal to zero and attempt to solve: Simplifying -472 + 16x2 + x4 = 0 Solving -472 + 16x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '472' to each side of the equation. -472 + 16x2 + 472 + x4 = 0 + 472 Reorder the terms: -472 + 472 + 16x2 + x4 = 0 + 472 Combine like terms: -472 + 472 = 0 0 + 16x2 + x4 = 0 + 472 16x2 + x4 = 0 + 472 Combine like terms: 0 + 472 = 472 16x2 + x4 = 472 The x term is 16x2. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x2 + 64 + x4 = 472 + 64 Reorder the terms: 64 + 16x2 + x4 = 472 + 64 Combine like terms: 472 + 64 = 536 64 + 16x2 + x4 = 536 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 536 Calculate the square root of the right side: 23.151673806 Break this problem into two subproblems by setting (x2 + 8) equal to 23.151673806 and -23.151673806.Subproblem 1
x2 + 8 = 23.151673806 Simplifying x2 + 8 = 23.151673806 Reorder the terms: 8 + x2 = 23.151673806 Solving 8 + x2 = 23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = 23.151673806 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 23.151673806 + -8 x2 = 23.151673806 + -8 Combine like terms: 23.151673806 + -8 = 15.151673806 x2 = 15.151673806 Simplifying x2 = 15.151673806 Take the square root of each side: x = {-3.8925151, 3.8925151}Subproblem 2
x2 + 8 = -23.151673806 Simplifying x2 + 8 = -23.151673806 Reorder the terms: 8 + x2 = -23.151673806 Solving 8 + x2 = -23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = -23.151673806 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -23.151673806 + -8 x2 = -23.151673806 + -8 Combine like terms: -23.151673806 + -8 = -31.151673806 x2 = -31.151673806 Simplifying x2 = -31.151673806 Reorder the terms: 31.151673806 + x2 = -31.151673806 + 31.151673806 Combine like terms: -31.151673806 + 31.151673806 = 0.000000000 31.151673806 + 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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