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Simplifying -2b3 + 12b2 + -14b = 0 Reorder the terms: -14b + 12b2 + -2b3 = 0 Solving -14b + 12b2 + -2b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b'. 2b(-7 + 6b + -1b2) = 0 Ignore the factor 2.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 '(-7 + 6b + -1b2)' equal to zero and attempt to solve: Simplifying -7 + 6b + -1b2 = 0 Solving -7 + 6b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -6b + b2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6b + -7 + b2 = 0 + -7 Reorder the terms: 7 + -7 + -6b + b2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6b + b2 = 0 + -7 -6b + b2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6b + b2 = -7 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = -7 + 9 Reorder the terms: 9 + -6b + b2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6b + b2 = 2 Factor a perfect square on the left side: (b + -3)(b + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (b + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
b + -3 = 1.414213562 Simplifying b + -3 = 1.414213562 Reorder the terms: -3 + b = 1.414213562 Solving -3 + b = 1.414213562 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + b = 1.414213562 + 3 b = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 b = 4.414213562 Simplifying b = 4.414213562Subproblem 2
b + -3 = -1.414213562 Simplifying b + -3 = -1.414213562 Reorder the terms: -3 + b = -1.414213562 Solving -3 + b = -1.414213562 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + b = -1.414213562 + 3 b = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 b = 1.585786438 Simplifying b = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.414213562, 1.585786438}Solution
b = {0, 4.414213562, 1.585786438}
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