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Simplifying x4 + 11x2 + -6 = 0 Reorder the terms: -6 + 11x2 + x4 = 0 Solving -6 + 11x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 11x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 11x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11x2 + x4 = 0 + 6 11x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 11x2 + x4 = 6 The x term is 11x2. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x2 + 30.25 + x4 = 6 + 30.25 Reorder the terms: 30.25 + 11x2 + x4 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + 11x2 + x4 = 36.25 Factor a perfect square on the left side: (x2 + 5.5)(x2 + 5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x2 + 5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x2 + 5.5 = 6.020797289 Simplifying x2 + 5.5 = 6.020797289 Reorder the terms: 5.5 + x2 = 6.020797289 Solving 5.5 + x2 = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = 6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = 6.020797289 + -5.5 x2 = 6.020797289 + -5.5 Combine like terms: 6.020797289 + -5.5 = 0.520797289 x2 = 0.520797289 Simplifying x2 = 0.520797289 Take the square root of each side: x = {-0.721662864, 0.721662864}Subproblem 2
x2 + 5.5 = -6.020797289 Simplifying x2 + 5.5 = -6.020797289 Reorder the terms: 5.5 + x2 = -6.020797289 Solving 5.5 + x2 = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x2 = -6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x2 = -6.020797289 + -5.5 x2 = -6.020797289 + -5.5 Combine like terms: -6.020797289 + -5.5 = -11.520797289 x2 = -11.520797289 Simplifying x2 = -11.520797289 Reorder the terms: 11.520797289 + x2 = -11.520797289 + 11.520797289 Combine like terms: -11.520797289 + 11.520797289 = 0.000000000 11.520797289 + 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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