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Simplifying 3b3 + 15b2 + -36b = 0 Reorder the terms: -36b + 15b2 + 3b3 = 0 Solving -36b + 15b2 + 3b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(-12 + 5b + b2) = 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 '(-12 + 5b + b2)' equal to zero and attempt to solve: Simplifying -12 + 5b + b2 = 0 Solving -12 + 5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 5b + 12 + b2 = 0 + 12 Reorder the terms: -12 + 12 + 5b + b2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5b + b2 = 0 + 12 5b + b2 = 0 + 12 Combine like terms: 0 + 12 = 12 5b + b2 = 12 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 = 12 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + 5b + b2 = 18.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (b + 2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
b + 2.5 = 4.272001873 Simplifying b + 2.5 = 4.272001873 Reorder the terms: 2.5 + b = 4.272001873 Solving 2.5 + b = 4.272001873 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 = 4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 4.272001873 + -2.5 b = 4.272001873 + -2.5 Combine like terms: 4.272001873 + -2.5 = 1.772001873 b = 1.772001873 Simplifying b = 1.772001873Subproblem 2
b + 2.5 = -4.272001873 Simplifying b + 2.5 = -4.272001873 Reorder the terms: 2.5 + b = -4.272001873 Solving 2.5 + b = -4.272001873 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 = -4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -4.272001873 + -2.5 b = -4.272001873 + -2.5 Combine like terms: -4.272001873 + -2.5 = -6.772001873 b = -6.772001873 Simplifying b = -6.772001873Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.772001873, -6.772001873}Solution
b = {0, 1.772001873, -6.772001873}
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