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Simplifying b(b2 + -12b + 1) = 0 Reorder the terms: b(1 + -12b + b2) = 0 (1 * b + -12b * b + b2 * b) = 0 (1b + -12b2 + b3) = 0 Solving 1b + -12b2 + b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(1 + -12b + b2) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(1 + -12b + b2)' equal to zero and attempt to solve: Simplifying 1 + -12b + b2 = 0 Solving 1 + -12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -12b + -1 + b2 = 0 + -1 Reorder the terms: 1 + -1 + -12b + b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12b + b2 = 0 + -1 -12b + b2 = 0 + -1 Combine like terms: 0 + -1 = -1 -12b + b2 = -1 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = -1 + 36 Reorder the terms: 36 + -12b + b2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + -12b + b2 = 35 Factor a perfect square on the left side: (b + -6)(b + -6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (b + -6) equal to 5.916079783 and -5.916079783.Subproblem 1
b + -6 = 5.916079783 Simplifying b + -6 = 5.916079783 Reorder the terms: -6 + b = 5.916079783 Solving -6 + b = 5.916079783 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + b = 5.916079783 + 6 b = 5.916079783 + 6 Combine like terms: 5.916079783 + 6 = 11.916079783 b = 11.916079783 Simplifying b = 11.916079783Subproblem 2
b + -6 = -5.916079783 Simplifying b + -6 = -5.916079783 Reorder the terms: -6 + b = -5.916079783 Solving -6 + b = -5.916079783 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + b = -5.916079783 + 6 b = -5.916079783 + 6 Combine like terms: -5.916079783 + 6 = 0.083920217 b = 0.083920217 Simplifying b = 0.083920217Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.916079783, 0.083920217}Solution
b = {0, 11.916079783, 0.083920217}
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