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Simplifying 2x5 + -4x3 + -4x = 0 Reorder the terms: -4x + -4x3 + 2x5 = 0 Solving -4x + -4x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-2 + -2x2 + 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 '(-2 + -2x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + -2x2 + x4 = 0 Solving -2 + -2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + -2x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2x2 + x4 = 0 + 2 -2x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 -2x2 + x4 = 2 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 2 + 1 Reorder the terms: 1 + -2x2 + x4 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2x2 + x4 = 3 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x2 + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
x2 + -1 = 1.732050808 Simplifying x2 + -1 = 1.732050808 Reorder the terms: -1 + x2 = 1.732050808 Solving -1 + x2 = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 1.732050808 + 1 x2 = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 x2 = 2.732050808 Simplifying x2 = 2.732050808 Take the square root of each side: x = {-1.65289165, 1.65289165}Subproblem 2
x2 + -1 = -1.732050808 Simplifying x2 + -1 = -1.732050808 Reorder the terms: -1 + x2 = -1.732050808 Solving -1 + x2 = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -1.732050808 + 1 x2 = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 x2 = -0.732050808 Simplifying x2 = -0.732050808 Reorder the terms: 0.732050808 + x2 = -0.732050808 + 0.732050808 Combine like terms: -0.732050808 + 0.732050808 = 0.000000000 0.732050808 + 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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