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Simplifying -1b(3b2 + 9b + -27) = 0 Reorder the terms: -1b(-27 + 9b + 3b2) = 0 (-27 * -1b + 9b * -1b + 3b2 * -1b) = 0 (27b + -9b2 + -3b3) = 0 Solving 27b + -9b2 + -3b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(9 + -3b + -1b2) = 0 Ignore the factor 3.Subproblem 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 '(9 + -3b + -1b2)' equal to zero and attempt to solve: Simplifying 9 + -3b + -1b2 = 0 Solving 9 + -3b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 3b + b2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 3b + 9 + b2 = 0 + 9 Reorder the terms: -9 + 9 + 3b + b2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3b + b2 = 0 + 9 3b + b2 = 0 + 9 Combine like terms: 0 + 9 = 9 3b + b2 = 9 The b term is 3b. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3b + 2.25 + b2 = 9 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + 3b + b2 = 11.25 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (b + 1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
b + 1.5 = 3.354101966 Simplifying b + 1.5 = 3.354101966 Reorder the terms: 1.5 + b = 3.354101966 Solving 1.5 + b = 3.354101966 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 3.354101966 + -1.5 b = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 b = 1.854101966 Simplifying b = 1.854101966Subproblem 2
b + 1.5 = -3.354101966 Simplifying b + 1.5 = -3.354101966 Reorder the terms: 1.5 + b = -3.354101966 Solving 1.5 + b = -3.354101966 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -3.354101966 + -1.5 b = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 b = -4.854101966 Simplifying b = -4.854101966Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.854101966, -4.854101966}Solution
b = {0, 1.854101966, -4.854101966}
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