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Simplifying x4 + 16x2 + -64 = 0 Reorder the terms: -64 + 16x2 + x4 = 0 Solving -64 + 16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 16x2 + 64 + x4 = 0 + 64 Reorder the terms: -64 + 64 + 16x2 + x4 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16x2 + x4 = 0 + 64 16x2 + x4 = 0 + 64 Combine like terms: 0 + 64 = 64 16x2 + x4 = 64 The x term is 16x2. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x2 + 64 + x4 = 64 + 64 Reorder the terms: 64 + 16x2 + x4 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + 16x2 + x4 = 128 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x2 + 8) equal to 11.313708499 and -11.313708499.Subproblem 1
x2 + 8 = 11.313708499 Simplifying x2 + 8 = 11.313708499 Reorder the terms: 8 + x2 = 11.313708499 Solving 8 + x2 = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 11.313708499 + -8 x2 = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 x2 = 3.313708499 Simplifying x2 = 3.313708499 Take the square root of each side: x = {-1.820359442, 1.820359442}Subproblem 2
x2 + 8 = -11.313708499 Simplifying x2 + 8 = -11.313708499 Reorder the terms: 8 + x2 = -11.313708499 Solving 8 + x2 = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -11.313708499 + -8 x2 = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 x2 = -19.313708499 Simplifying x2 = -19.313708499 Reorder the terms: 19.313708499 + x2 = -19.313708499 + 19.313708499 Combine like terms: -19.313708499 + 19.313708499 = 0.000000000 19.313708499 + 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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