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Simplifying x4 + 8x2 + -4 = 0 Reorder the terms: -4 + 8x2 + x4 = 0 Solving -4 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 8x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + 8x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8x2 + x4 = 0 + 4 8x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 8x2 + x4 = 4 The x term is 8x2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x2 + 16 + x4 = 4 + 16 Reorder the terms: 16 + 8x2 + x4 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8x2 + x4 = 20 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x2 + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
x2 + 4 = 4.472135955 Simplifying x2 + 4 = 4.472135955 Reorder the terms: 4 + x2 = 4.472135955 Solving 4 + x2 = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.472135955 + -4 x2 = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 x2 = 0.472135955 Simplifying x2 = 0.472135955 Take the square root of each side: x = {-0.687121499, 0.687121499}Subproblem 2
x2 + 4 = -4.472135955 Simplifying x2 + 4 = -4.472135955 Reorder the terms: 4 + x2 = -4.472135955 Solving 4 + x2 = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.472135955 + -4 x2 = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 x2 = -8.472135955 Simplifying x2 = -8.472135955 Reorder the terms: 8.472135955 + x2 = -8.472135955 + 8.472135955 Combine like terms: -8.472135955 + 8.472135955 = 0.000000000 8.472135955 + 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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