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Simplifying x4 + 4x2 + -28 = 0 Reorder the terms: -28 + 4x2 + x4 = 0 Solving -28 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 4x2 + 28 + x4 = 0 + 28 Reorder the terms: -28 + 28 + 4x2 + x4 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 4x2 + x4 = 0 + 28 4x2 + x4 = 0 + 28 Combine like terms: 0 + 28 = 28 4x2 + x4 = 28 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 = 28 + 4 Reorder the terms: 4 + 4x2 + x4 = 28 + 4 Combine like terms: 28 + 4 = 32 4 + 4x2 + x4 = 32 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + 2) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + 2 = 5.656854249 Simplifying x2 + 2 = 5.656854249 Reorder the terms: 2 + x2 = 5.656854249 Solving 2 + x2 = 5.656854249 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 = 5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 5.656854249 + -2 x2 = 5.656854249 + -2 Combine like terms: 5.656854249 + -2 = 3.656854249 x2 = 3.656854249 Simplifying x2 = 3.656854249 Take the square root of each side: x = {-1.912290315, 1.912290315}Subproblem 2
x2 + 2 = -5.656854249 Simplifying x2 + 2 = -5.656854249 Reorder the terms: 2 + x2 = -5.656854249 Solving 2 + x2 = -5.656854249 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 = -5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -5.656854249 + -2 x2 = -5.656854249 + -2 Combine like terms: -5.656854249 + -2 = -7.656854249 x2 = -7.656854249 Simplifying x2 = -7.656854249 Reorder the terms: 7.656854249 + x2 = -7.656854249 + 7.656854249 Combine like terms: -7.656854249 + 7.656854249 = 0.000000000 7.656854249 + 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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