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Simplifying 2x4 + 8x2 + 4 = 0 Reorder the terms: 4 + 8x2 + 2x4 = 0 Solving 4 + 8x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 4x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying 2 + 4x2 + x4 = 0 Solving 2 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + 4x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4x2 + x4 = 0 + -2 4x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 4x2 + x4 = -2 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = -2 + 4 Reorder the terms: 4 + 4x2 + x4 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + 4x2 + x4 = 2 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + 2 = 1.414213562 Simplifying x2 + 2 = 1.414213562 Reorder the terms: 2 + x2 = 1.414213562 Solving 2 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 1.414213562 + -2 x2 = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 x2 = -0.585786438 Simplifying x2 = -0.585786438 Reorder the terms: 0.585786438 + x2 = -0.585786438 + 0.585786438 Combine like terms: -0.585786438 + 0.585786438 = 0.000000000 0.585786438 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 2 = -1.414213562 Simplifying x2 + 2 = -1.414213562 Reorder the terms: 2 + x2 = -1.414213562 Solving 2 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -1.414213562 + -2 x2 = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 x2 = -3.414213562 Simplifying x2 = -3.414213562 Reorder the terms: 3.414213562 + x2 = -3.414213562 + 3.414213562 Combine like terms: -3.414213562 + 3.414213562 = 0.000000000 3.414213562 + 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. The solution to this equation could not be determined.
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