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Simplifying x4 + -0.4x2 + -0.234567 = 0 Reorder the terms: -0.234567 + -0.4x2 + x4 = 0 Solving -0.234567 + -0.4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.234567' to each side of the equation. -0.234567 + -0.4x2 + 0.234567 + x4 = 0 + 0.234567 Reorder the terms: -0.234567 + 0.234567 + -0.4x2 + x4 = 0 + 0.234567 Combine like terms: -0.234567 + 0.234567 = 0.000000 0.000000 + -0.4x2 + x4 = 0 + 0.234567 -0.4x2 + x4 = 0 + 0.234567 Combine like terms: 0 + 0.234567 = 0.234567 -0.4x2 + x4 = 0.234567 The x term is -0.4x2. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x2 + 0.04 + x4 = 0.234567 + 0.04 Reorder the terms: 0.04 + -0.4x2 + x4 = 0.234567 + 0.04 Combine like terms: 0.234567 + 0.04 = 0.274567 0.04 + -0.4x2 + x4 = 0.274567 Factor a perfect square on the left side: (x2 + -0.2)(x2 + -0.2) = 0.274567 Calculate the square root of the right side: 0.523991412 Break this problem into two subproblems by setting (x2 + -0.2) equal to 0.523991412 and -0.523991412.Subproblem 1
x2 + -0.2 = 0.523991412 Simplifying x2 + -0.2 = 0.523991412 Reorder the terms: -0.2 + x2 = 0.523991412 Solving -0.2 + x2 = 0.523991412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x2 = 0.523991412 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x2 = 0.523991412 + 0.2 x2 = 0.523991412 + 0.2 Combine like terms: 0.523991412 + 0.2 = 0.723991412 x2 = 0.723991412 Simplifying x2 = 0.723991412 Take the square root of each side: x = {-0.850876849, 0.850876849}Subproblem 2
x2 + -0.2 = -0.523991412 Simplifying x2 + -0.2 = -0.523991412 Reorder the terms: -0.2 + x2 = -0.523991412 Solving -0.2 + x2 = -0.523991412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x2 = -0.523991412 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x2 = -0.523991412 + 0.2 x2 = -0.523991412 + 0.2 Combine like terms: -0.523991412 + 0.2 = -0.323991412 x2 = -0.323991412 Simplifying x2 = -0.323991412 Reorder the terms: 0.323991412 + x2 = -0.323991412 + 0.323991412 Combine like terms: -0.323991412 + 0.323991412 = 0.000000000 0.323991412 + 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.
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