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Simplifying x6 + -5x2 + -2x4 = 0 Reorder the terms: -5x2 + -2x4 + x6 = 0 Solving -5x2 + -2x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-5 + -2x2 + x4) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-5 + -2x2 + x4)' equal to zero and attempt to solve: Simplifying -5 + -2x2 + x4 = 0 Solving -5 + -2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -2x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x2 + x4 = 0 + 5 -2x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x2 + x4 = 5 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 = 5 + 1 Reorder the terms: 1 + -2x2 + x4 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -1 = 2.449489743 Simplifying x2 + -1 = 2.449489743 Reorder the terms: -1 + x2 = 2.449489743 Solving -1 + x2 = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 2.449489743 + 1 x2 = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x2 = 3.449489743 Simplifying x2 = 3.449489743 Take the square root of each side: x = {-1.8572802, 1.8572802}Subproblem 2
x2 + -1 = -2.449489743 Simplifying x2 + -1 = -2.449489743 Reorder the terms: -1 + x2 = -2.449489743 Solving -1 + x2 = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -2.449489743 + 1 x2 = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x2 = -1.449489743 Simplifying x2 = -1.449489743 Reorder the terms: 1.449489743 + x2 = -1.449489743 + 1.449489743 Combine like terms: -1.449489743 + 1.449489743 = 0.000000000 1.449489743 + 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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