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Simplifying b(b2 + -5b + -16) = 0 Reorder the terms: b(-16 + -5b + b2) = 0 (-16 * b + -5b * b + b2 * b) = 0 (-16b + -5b2 + b3) = 0 Solving -16b + -5b2 + b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(-16 + -5b + 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 + -5b + b2)' equal to zero and attempt to solve: Simplifying -16 + -5b + b2 = 0 Solving -16 + -5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -5b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -5b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5b + b2 = 0 + 16 -5b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5b + b2 = 16 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = 16 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + -5b + b2 = 22.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (b + -2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
b + -2.5 = 4.716990566 Simplifying b + -2.5 = 4.716990566 Reorder the terms: -2.5 + b = 4.716990566 Solving -2.5 + b = 4.716990566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 4.716990566 + 2.5 b = 4.716990566 + 2.5 Combine like terms: 4.716990566 + 2.5 = 7.216990566 b = 7.216990566 Simplifying b = 7.216990566Subproblem 2
b + -2.5 = -4.716990566 Simplifying b + -2.5 = -4.716990566 Reorder the terms: -2.5 + b = -4.716990566 Solving -2.5 + b = -4.716990566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -4.716990566 + 2.5 b = -4.716990566 + 2.5 Combine like terms: -4.716990566 + 2.5 = -2.216990566 b = -2.216990566 Simplifying b = -2.216990566Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.216990566, -2.216990566}Solution
b = {0, 7.216990566, -2.216990566}
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