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Simplifying 1.3(8 + -1b) * 3.7b = -5.2 Reorder the terms for easier multiplication: 1.3 * 3.7b(8 + -1b) = -5.2 Multiply 1.3 * 3.7 4.81b(8 + -1b) = -5.2 (8 * 4.81b + -1b * 4.81b) = -5.2 (38.48b + -4.81b2) = -5.2 Solving 38.48b + -4.81b2 = -5.2 Solving for variable 'b'. Reorder the terms: 5.2 + 38.48b + -4.81b2 = -5.2 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 5.2 + 38.48b + -4.81b2 = 0.0 Begin completing the square. Divide all terms by -4.81 the coefficient of the squared term: Divide each side by '-4.81'. -1.081081081 + -8b + b2 = 0 Move the constant term to the right: Add '1.081081081' to each side of the equation. -1.081081081 + -8b + 1.081081081 + b2 = 0 + 1.081081081 Reorder the terms: -1.081081081 + 1.081081081 + -8b + b2 = 0 + 1.081081081 Combine like terms: -1.081081081 + 1.081081081 = 0.000000000 0.000000000 + -8b + b2 = 0 + 1.081081081 -8b + b2 = 0 + 1.081081081 Combine like terms: 0 + 1.081081081 = 1.081081081 -8b + b2 = 1.081081081 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = 1.081081081 + 16 Reorder the terms: 16 + -8b + b2 = 1.081081081 + 16 Combine like terms: 1.081081081 + 16 = 17.081081081 16 + -8b + b2 = 17.081081081 Factor a perfect square on the left side: (b + -4)(b + -4) = 17.081081081 Calculate the square root of the right side: 4.132926455 Break this problem into two subproblems by setting (b + -4) equal to 4.132926455 and -4.132926455.Subproblem 1
b + -4 = 4.132926455 Simplifying b + -4 = 4.132926455 Reorder the terms: -4 + b = 4.132926455 Solving -4 + b = 4.132926455 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 4.132926455 + 4 Combine like terms: -4 + 4 = 0 0 + b = 4.132926455 + 4 b = 4.132926455 + 4 Combine like terms: 4.132926455 + 4 = 8.132926455 b = 8.132926455 Simplifying b = 8.132926455Subproblem 2
b + -4 = -4.132926455 Simplifying b + -4 = -4.132926455 Reorder the terms: -4 + b = -4.132926455 Solving -4 + b = -4.132926455 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -4.132926455 + 4 Combine like terms: -4 + 4 = 0 0 + b = -4.132926455 + 4 b = -4.132926455 + 4 Combine like terms: -4.132926455 + 4 = -0.132926455 b = -0.132926455 Simplifying b = -0.132926455Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.132926455, -0.132926455}
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