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Simplifying (x4 + 13x2 + 9) = 0 Reorder the terms: (9 + 13x2 + x4) = 0 Remove parenthesis around (9 + 13x2 + x4) 9 + 13x2 + x4 = 0 Solving 9 + 13x2 + 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 + 13x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + 13x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 13x2 + x4 = 0 + -9 13x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 13x2 + x4 = -9 The x term is 13x2. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x2 + 42.25 + x4 = -9 + 42.25 Reorder the terms: 42.25 + 13x2 + x4 = -9 + 42.25 Combine like terms: -9 + 42.25 = 33.25 42.25 + 13x2 + x4 = 33.25 Factor a perfect square on the left side: (x2 + 6.5)(x2 + 6.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x2 + 6.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x2 + 6.5 = 5.766281297 Simplifying x2 + 6.5 = 5.766281297 Reorder the terms: 6.5 + x2 = 5.766281297 Solving 6.5 + x2 = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x2 = 5.766281297 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x2 = 5.766281297 + -6.5 x2 = 5.766281297 + -6.5 Combine like terms: 5.766281297 + -6.5 = -0.733718703 x2 = -0.733718703 Simplifying x2 = -0.733718703 Reorder the terms: 0.733718703 + x2 = -0.733718703 + 0.733718703 Combine like terms: -0.733718703 + 0.733718703 = 0.000000000 0.733718703 + 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 + 6.5 = -5.766281297 Simplifying x2 + 6.5 = -5.766281297 Reorder the terms: 6.5 + x2 = -5.766281297 Solving 6.5 + x2 = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x2 = -5.766281297 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x2 = -5.766281297 + -6.5 x2 = -5.766281297 + -6.5 Combine like terms: -5.766281297 + -6.5 = -12.266281297 x2 = -12.266281297 Simplifying x2 = -12.266281297 Reorder the terms: 12.266281297 + x2 = -12.266281297 + 12.266281297 Combine like terms: -12.266281297 + 12.266281297 = 0.000000000 12.266281297 + 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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