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Simplifying b4 + -1b2 + -36 = 0 Reorder the terms: -36 + -1b2 + b4 = 0 Solving -36 + -1b2 + b4 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -1b2 + 36 + b4 = 0 + 36 Reorder the terms: -36 + 36 + -1b2 + b4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1b2 + b4 = 0 + 36 -1b2 + b4 = 0 + 36 Combine like terms: 0 + 36 = 36 -1b2 + b4 = 36 The b term is -1b2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b2 + 0.25 + b4 = 36 + 0.25 Reorder the terms: 0.25 + -1b2 + b4 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + -1b2 + b4 = 36.25 Factor a perfect square on the left side: (b2 + -0.5)(b2 + -0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (b2 + -0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
b2 + -0.5 = 6.020797289 Simplifying b2 + -0.5 = 6.020797289 Reorder the terms: -0.5 + b2 = 6.020797289 Solving -0.5 + b2 = 6.020797289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b2 = 6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b2 = 6.020797289 + 0.5 b2 = 6.020797289 + 0.5 Combine like terms: 6.020797289 + 0.5 = 6.520797289 b2 = 6.520797289 Simplifying b2 = 6.520797289 Take the square root of each side: b = {-2.553585183, 2.553585183}Subproblem 2
b2 + -0.5 = -6.020797289 Simplifying b2 + -0.5 = -6.020797289 Reorder the terms: -0.5 + b2 = -6.020797289 Solving -0.5 + b2 = -6.020797289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b2 = -6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b2 = -6.020797289 + 0.5 b2 = -6.020797289 + 0.5 Combine like terms: -6.020797289 + 0.5 = -5.520797289 b2 = -5.520797289 Simplifying b2 = -5.520797289 Reorder the terms: 5.520797289 + b2 = -5.520797289 + 5.520797289 Combine like terms: -5.520797289 + 5.520797289 = 0.000000000 5.520797289 + b2 = 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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