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Simplifying x4 + 8x2 + -16 = 0 Reorder the terms: -16 + 8x2 + x4 = 0 Solving -16 + 8x2 + 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 + 8x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 8x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8x2 + x4 = 0 + 16 8x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 8x2 + x4 = 16 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 = 16 + 16 Reorder the terms: 16 + 8x2 + x4 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8x2 + x4 = 32 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + 4 = 5.656854249 Simplifying x2 + 4 = 5.656854249 Reorder the terms: 4 + x2 = 5.656854249 Solving 4 + x2 = 5.656854249 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 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 5.656854249 + -4 x2 = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 x2 = 1.656854249 Simplifying x2 = 1.656854249 Take the square root of each side: x = {-1.287188506, 1.287188506}Subproblem 2
x2 + 4 = -5.656854249 Simplifying x2 + 4 = -5.656854249 Reorder the terms: 4 + x2 = -5.656854249 Solving 4 + x2 = -5.656854249 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 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -5.656854249 + -4 x2 = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 x2 = -9.656854249 Simplifying x2 = -9.656854249 Reorder the terms: 9.656854249 + x2 = -9.656854249 + 9.656854249 Combine like terms: -9.656854249 + 9.656854249 = 0.000000000 9.656854249 + 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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