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Simplifying b3 + -8b2 = 16b Reorder the terms: -8b2 + b3 = 16b Solving -8b2 + b3 = 16b Solving for variable 'b'. Reorder the terms: -16b + -8b2 + b3 = 16b + -16b Combine like terms: 16b + -16b = 0 -16b + -8b2 + b3 = 0 Factor out the Greatest Common Factor (GCF), 'b'. b(-16 + -8b + 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 '(-16 + -8b + b2)' equal to zero and attempt to solve: Simplifying -16 + -8b + b2 = 0 Solving -16 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -8b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8b + b2 = 0 + 16 -8b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8b + b2 = 16 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = 16 + 16 Reorder the terms: 16 + -8b + b2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8b + b2 = 32 Factor a perfect square on the left side: (b + -4)(b + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (b + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
b + -4 = 5.656854249 Simplifying b + -4 = 5.656854249 Reorder the terms: -4 + b = 5.656854249 Solving -4 + b = 5.656854249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + b = 5.656854249 + 4 b = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 b = 9.656854249 Simplifying b = 9.656854249Subproblem 2
b + -4 = -5.656854249 Simplifying b + -4 = -5.656854249 Reorder the terms: -4 + b = -5.656854249 Solving -4 + b = -5.656854249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + b = -5.656854249 + 4 b = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 b = -1.656854249 Simplifying b = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.656854249, -1.656854249}Solution
b = {0, 9.656854249, -1.656854249}
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