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Simplifying x4 + 4x2 + -16 = 0 Reorder the terms: -16 + 4x2 + x4 = 0 Solving -16 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 4x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4x2 + x4 = 0 + 16 4x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 4x2 + x4 = 16 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 = 16 + 4 Reorder the terms: 4 + 4x2 + x4 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4x2 + x4 = 20 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x2 + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
x2 + 2 = 4.472135955 Simplifying x2 + 2 = 4.472135955 Reorder the terms: 2 + x2 = 4.472135955 Solving 2 + x2 = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 4.472135955 + -2 x2 = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 x2 = 2.472135955 Simplifying x2 = 2.472135955 Take the square root of each side: x = {-1.572302756, 1.572302756}Subproblem 2
x2 + 2 = -4.472135955 Simplifying x2 + 2 = -4.472135955 Reorder the terms: 2 + x2 = -4.472135955 Solving 2 + x2 = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -4.472135955 + -2 x2 = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 x2 = -6.472135955 Simplifying x2 = -6.472135955 Reorder the terms: 6.472135955 + x2 = -6.472135955 + 6.472135955 Combine like terms: -6.472135955 + 6.472135955 = 0.000000000 6.472135955 + 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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