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Simplifying b4 + -1b3 + -3b2 = 0 Reorder the terms: -3b2 + -1b3 + b4 = 0 Solving -3b2 + -1b3 + b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b2'. b2(-3 + -1b + b2) = 0Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(-3 + -1b + b2)' equal to zero and attempt to solve: Simplifying -3 + -1b + b2 = 0 Solving -3 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + -1b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b + b2 = 0 + 3 -1b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1b + b2 = 3 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 3 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1b + b2 = 3.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (b + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
b + -0.5 = 1.802775638 Simplifying b + -0.5 = 1.802775638 Reorder the terms: -0.5 + b = 1.802775638 Solving -0.5 + b = 1.802775638 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 1.802775638 + 0.5 b = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 b = 2.302775638 Simplifying b = 2.302775638Subproblem 2
b + -0.5 = -1.802775638 Simplifying b + -0.5 = -1.802775638 Reorder the terms: -0.5 + b = -1.802775638 Solving -0.5 + b = -1.802775638 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -1.802775638 + 0.5 b = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 b = -1.302775638 Simplifying b = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.302775638, -1.302775638}Solution
b = {0, 2.302775638, -1.302775638}
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