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Simplifying 5b3 + 34b2 + 7b = 0 Reorder the terms: 7b + 34b2 + 5b3 = 0 Solving 7b + 34b2 + 5b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(7 + 34b + 5b2) = 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 '(7 + 34b + 5b2)' equal to zero and attempt to solve: Simplifying 7 + 34b + 5b2 = 0 Solving 7 + 34b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 6.8b + b2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 6.8b + -1.4 + b2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 6.8b + b2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 6.8b + b2 = 0 + -1.4 6.8b + b2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 6.8b + b2 = -1.4 The b term is 6.8b. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8b + 11.56 + b2 = -1.4 + 11.56 Reorder the terms: 11.56 + 6.8b + b2 = -1.4 + 11.56 Combine like terms: -1.4 + 11.56 = 10.16 11.56 + 6.8b + b2 = 10.16 Factor a perfect square on the left side: (b + 3.4)(b + 3.4) = 10.16 Calculate the square root of the right side: 3.18747549 Break this problem into two subproblems by setting (b + 3.4) equal to 3.18747549 and -3.18747549.Subproblem 1
b + 3.4 = 3.18747549 Simplifying b + 3.4 = 3.18747549 Reorder the terms: 3.4 + b = 3.18747549 Solving 3.4 + b = 3.18747549 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + b = 3.18747549 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + b = 3.18747549 + -3.4 b = 3.18747549 + -3.4 Combine like terms: 3.18747549 + -3.4 = -0.21252451 b = -0.21252451 Simplifying b = -0.21252451Subproblem 2
b + 3.4 = -3.18747549 Simplifying b + 3.4 = -3.18747549 Reorder the terms: 3.4 + b = -3.18747549 Solving 3.4 + b = -3.18747549 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + b = -3.18747549 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + b = -3.18747549 + -3.4 b = -3.18747549 + -3.4 Combine like terms: -3.18747549 + -3.4 = -6.58747549 b = -6.58747549 Simplifying b = -6.58747549Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.21252451, -6.58747549}Solution
b = {0, -0.21252451, -6.58747549}
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