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Simplifying 35b2 + -10b + -5 = 0 Reorder the terms: -5 + -10b + 35b2 = 0 Solving -5 + -10b + 35b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -2b + 7b2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -2b + 7b2)' equal to zero and attempt to solve: Simplifying -1 + -2b + 7b2 = 0 Solving -1 + -2b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857b + b2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857b + 0.1428571429 + b2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857b + b2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857b + b2 = 0 + 0.1428571429 -0.2857142857b + b2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857b + b2 = 0.1428571429 The b term is -0.2857142857b. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857b + 0.02040816328 + b2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857b + b2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857b + b2 = 0.16326530618 Factor a perfect square on the left side: (b + -0.1428571429)(b + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (b + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
b + -0.1428571429 = 0.404061018 Simplifying b + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + b = 0.404061018 Solving -0.1428571429 + b = 0.404061018 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + b = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = 0.404061018 + 0.1428571429 b = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 b = 0.5469181609 Simplifying b = 0.5469181609Subproblem 2
b + -0.1428571429 = -0.404061018 Simplifying b + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + b = -0.404061018 Solving -0.1428571429 + b = -0.404061018 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + b = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + b = -0.404061018 + 0.1428571429 b = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 b = -0.2612038751 Simplifying b = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.5469181609, -0.2612038751}Solution
b = {0.5469181609, -0.2612038751}
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