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Simplifying x4 + -32x2 + 128 = 0 Reorder the terms: 128 + -32x2 + x4 = 0 Solving 128 + -32x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-128' to each side of the equation. 128 + -32x2 + -128 + x4 = 0 + -128 Reorder the terms: 128 + -128 + -32x2 + x4 = 0 + -128 Combine like terms: 128 + -128 = 0 0 + -32x2 + x4 = 0 + -128 -32x2 + x4 = 0 + -128 Combine like terms: 0 + -128 = -128 -32x2 + x4 = -128 The x term is -32x2. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x2 + 256 + x4 = -128 + 256 Reorder the terms: 256 + -32x2 + x4 = -128 + 256 Combine like terms: -128 + 256 = 128 256 + -32x2 + x4 = 128 Factor a perfect square on the left side: (x2 + -16)(x2 + -16) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x2 + -16) equal to 11.313708499 and -11.313708499.Subproblem 1
x2 + -16 = 11.313708499 Simplifying x2 + -16 = 11.313708499 Reorder the terms: -16 + x2 = 11.313708499 Solving -16 + x2 = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = 11.313708499 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 11.313708499 + 16 x2 = 11.313708499 + 16 Combine like terms: 11.313708499 + 16 = 27.313708499 x2 = 27.313708499 Simplifying x2 = 27.313708499 Take the square root of each side: x = {-5.22625186, 5.22625186}Subproblem 2
x2 + -16 = -11.313708499 Simplifying x2 + -16 = -11.313708499 Reorder the terms: -16 + x2 = -11.313708499 Solving -16 + x2 = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = -11.313708499 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -11.313708499 + 16 x2 = -11.313708499 + 16 Combine like terms: -11.313708499 + 16 = 4.686291501 x2 = 4.686291501 Simplifying x2 = 4.686291501 Take the square root of each side: x = {-2.164784401, 2.164784401}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.22625186, 5.22625186, -2.164784401, 2.164784401}
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