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Simplifying x4 + -3x2 + -27 = 0 Reorder the terms: -27 + -3x2 + x4 = 0 Solving -27 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -3x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + -3x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -3x2 + x4 = 0 + 27 -3x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 -3x2 + x4 = 27 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 27 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 27 + 2.25 Combine like terms: 27 + 2.25 = 29.25 2.25 + -3x2 + x4 = 29.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x2 + -1.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x2 + -1.5 = 5.408326913 Simplifying x2 + -1.5 = 5.408326913 Reorder the terms: -1.5 + x2 = 5.408326913 Solving -1.5 + x2 = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 5.408326913 + 1.5 x2 = 5.408326913 + 1.5 Combine like terms: 5.408326913 + 1.5 = 6.908326913 x2 = 6.908326913 Simplifying x2 = 6.908326913 Take the square root of each side: x = {-2.62836963, 2.62836963}Subproblem 2
x2 + -1.5 = -5.408326913 Simplifying x2 + -1.5 = -5.408326913 Reorder the terms: -1.5 + x2 = -5.408326913 Solving -1.5 + x2 = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -5.408326913 + 1.5 x2 = -5.408326913 + 1.5 Combine like terms: -5.408326913 + 1.5 = -3.908326913 x2 = -3.908326913 Simplifying x2 = -3.908326913 Reorder the terms: 3.908326913 + x2 = -3.908326913 + 3.908326913 Combine like terms: -3.908326913 + 3.908326913 = 0.000000000 3.908326913 + 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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