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Simplifying x4 + -4x2 + -8 = 0 Reorder the terms: -8 + -4x2 + x4 = 0 Solving -8 + -4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -4x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4x2 + x4 = 0 + 8 -4x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -4x2 + x4 = 8 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 = 8 + 4 Reorder the terms: 4 + -4x2 + x4 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4x2 + x4 = 12 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x2 + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
x2 + -2 = 3.464101615 Simplifying x2 + -2 = 3.464101615 Reorder the terms: -2 + x2 = 3.464101615 Solving -2 + x2 = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 3.464101615 + 2 x2 = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 x2 = 5.464101615 Simplifying x2 = 5.464101615 Take the square root of each side: x = {-2.337541789, 2.337541789}Subproblem 2
x2 + -2 = -3.464101615 Simplifying x2 + -2 = -3.464101615 Reorder the terms: -2 + x2 = -3.464101615 Solving -2 + x2 = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -3.464101615 + 2 x2 = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 x2 = -1.464101615 Simplifying x2 = -1.464101615 Reorder the terms: 1.464101615 + x2 = -1.464101615 + 1.464101615 Combine like terms: -1.464101615 + 1.464101615 = 0.000000000 1.464101615 + 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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