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Simplifying 2(x6) + 5(x4) + -1x2 = 0 Reorder the terms: -1x2 + 5x4 + 2x6 = 0 Solving -1x2 + 5x4 + 2x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + 5x2 + 2x4) = 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 '(-1 + 5x2 + 2x4)' equal to zero and attempt to solve: Simplifying -1 + 5x2 + 2x4 = 0 Solving -1 + 5x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 2.5x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.5x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.5x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.5x2 + x4 = 0 + 0.5 2.5x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.5x2 + x4 = 0.5 The x term is 2.5x2. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x2 + 1.5625 + x4 = 0.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x2 + x4 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + 2.5x2 + x4 = 2.0625 Factor a perfect square on the left side: (x2 + 1.25)(x2 + 1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x2 + 1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x2 + 1.25 = 1.436140662 Simplifying x2 + 1.25 = 1.436140662 Reorder the terms: 1.25 + x2 = 1.436140662 Solving 1.25 + x2 = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = 1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = 1.436140662 + -1.25 x2 = 1.436140662 + -1.25 Combine like terms: 1.436140662 + -1.25 = 0.186140662 x2 = 0.186140662 Simplifying x2 = 0.186140662 Take the square root of each side: x = {-0.431440218, 0.431440218}Subproblem 2
x2 + 1.25 = -1.436140662 Simplifying x2 + 1.25 = -1.436140662 Reorder the terms: 1.25 + x2 = -1.436140662 Solving 1.25 + x2 = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = -1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = -1.436140662 + -1.25 x2 = -1.436140662 + -1.25 Combine like terms: -1.436140662 + -1.25 = -2.686140662 x2 = -2.686140662 Simplifying x2 = -2.686140662 Reorder the terms: 2.686140662 + x2 = -2.686140662 + 2.686140662 Combine like terms: -2.686140662 + 2.686140662 = 0.000000000 2.686140662 + 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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