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Simplifying x4 + 9x2 + 9 = 0 Reorder the terms: 9 + 9x2 + x4 = 0 Solving 9 + 9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 9x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + 9x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 9x2 + x4 = 0 + -9 9x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 9x2 + x4 = -9 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = -9 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + 9x2 + x4 = 11.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x2 + 4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x2 + 4.5 = 3.354101966 Simplifying x2 + 4.5 = 3.354101966 Reorder the terms: 4.5 + x2 = 3.354101966 Solving 4.5 + x2 = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 3.354101966 + -4.5 x2 = 3.354101966 + -4.5 Combine like terms: 3.354101966 + -4.5 = -1.145898034 x2 = -1.145898034 Simplifying x2 = -1.145898034 Reorder the terms: 1.145898034 + x2 = -1.145898034 + 1.145898034 Combine like terms: -1.145898034 + 1.145898034 = 0.000000000 1.145898034 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 4.5 = -3.354101966 Simplifying x2 + 4.5 = -3.354101966 Reorder the terms: 4.5 + x2 = -3.354101966 Solving 4.5 + x2 = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -3.354101966 + -4.5 x2 = -3.354101966 + -4.5 Combine like terms: -3.354101966 + -4.5 = -7.854101966 x2 = -7.854101966 Simplifying x2 = -7.854101966 Reorder the terms: 7.854101966 + x2 = -7.854101966 + 7.854101966 Combine like terms: -7.854101966 + 7.854101966 = 0.000000000 7.854101966 + 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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