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Simplifying 2x4 + -132x2 = 256 Reorder the terms: -132x2 + 2x4 = 256 Solving -132x2 + 2x4 = 256 Solving for variable 'x'. Reorder the terms: -256 + -132x2 + 2x4 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + -132x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-128 + -66x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-128 + -66x2 + x4)' equal to zero and attempt to solve: Simplifying -128 + -66x2 + x4 = 0 Solving -128 + -66x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + -66x2 + 128 + x4 = 0 + 128 Reorder the terms: -128 + 128 + -66x2 + x4 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -66x2 + x4 = 0 + 128 -66x2 + x4 = 0 + 128 Combine like terms: 0 + 128 = 128 -66x2 + x4 = 128 The x term is -66x2. Take half its coefficient (-33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. -66x2 + 1089 + x4 = 128 + 1089 Reorder the terms: 1089 + -66x2 + x4 = 128 + 1089 Combine like terms: 128 + 1089 = 1217 1089 + -66x2 + x4 = 1217 Factor a perfect square on the left side: (x2 + -33)(x2 + -33) = 1217 Calculate the square root of the right side: 34.885527085 Break this problem into two subproblems by setting (x2 + -33) equal to 34.885527085 and -34.885527085.Subproblem 1
x2 + -33 = 34.885527085 Simplifying x2 + -33 = 34.885527085 Reorder the terms: -33 + x2 = 34.885527085 Solving -33 + x2 = 34.885527085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x2 = 34.885527085 + 33 Combine like terms: -33 + 33 = 0 0 + x2 = 34.885527085 + 33 x2 = 34.885527085 + 33 Combine like terms: 34.885527085 + 33 = 67.885527085 x2 = 67.885527085 Simplifying x2 = 67.885527085 Take the square root of each side: x = {-8.239267388, 8.239267388}Subproblem 2
x2 + -33 = -34.885527085 Simplifying x2 + -33 = -34.885527085 Reorder the terms: -33 + x2 = -34.885527085 Solving -33 + x2 = -34.885527085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x2 = -34.885527085 + 33 Combine like terms: -33 + 33 = 0 0 + x2 = -34.885527085 + 33 x2 = -34.885527085 + 33 Combine like terms: -34.885527085 + 33 = -1.885527085 x2 = -1.885527085 Simplifying x2 = -1.885527085 Reorder the terms: 1.885527085 + x2 = -1.885527085 + 1.885527085 Combine like terms: -1.885527085 + 1.885527085 = 0.000000000 1.885527085 + 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. 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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