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Simplifying -5b(b + -6) = -2(b + -9) + 3b Reorder the terms: -5b(-6 + b) = -2(b + -9) + 3b (-6 * -5b + b * -5b) = -2(b + -9) + 3b (30b + -5b2) = -2(b + -9) + 3b Reorder the terms: 30b + -5b2 = -2(-9 + b) + 3b 30b + -5b2 = (-9 * -2 + b * -2) + 3b 30b + -5b2 = (18 + -2b) + 3b Combine like terms: -2b + 3b = 1b 30b + -5b2 = 18 + 1b Solving 30b + -5b2 = 18 + 1b Solving for variable 'b'. Reorder the terms: -18 + 30b + -1b + -5b2 = 18 + 1b + -18 + -1b Combine like terms: 30b + -1b = 29b -18 + 29b + -5b2 = 18 + 1b + -18 + -1b Reorder the terms: -18 + 29b + -5b2 = 18 + -18 + 1b + -1b Combine like terms: 18 + -18 = 0 -18 + 29b + -5b2 = 0 + 1b + -1b -18 + 29b + -5b2 = 1b + -1b Combine like terms: 1b + -1b = 0 -18 + 29b + -5b2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.6 + -5.8b + b2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -5.8b + -3.6 + b2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -5.8b + b2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -5.8b + b2 = 0 + -3.6 -5.8b + b2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -5.8b + b2 = -3.6 The b term is -5.8b. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8b + 8.41 + b2 = -3.6 + 8.41 Reorder the terms: 8.41 + -5.8b + b2 = -3.6 + 8.41 Combine like terms: -3.6 + 8.41 = 4.81 8.41 + -5.8b + b2 = 4.81 Factor a perfect square on the left side: (b + -2.9)(b + -2.9) = 4.81 Calculate the square root of the right side: 2.19317122 Break this problem into two subproblems by setting (b + -2.9) equal to 2.19317122 and -2.19317122.Subproblem 1
b + -2.9 = 2.19317122 Simplifying b + -2.9 = 2.19317122 Reorder the terms: -2.9 + b = 2.19317122 Solving -2.9 + b = 2.19317122 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + b = 2.19317122 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + b = 2.19317122 + 2.9 b = 2.19317122 + 2.9 Combine like terms: 2.19317122 + 2.9 = 5.09317122 b = 5.09317122 Simplifying b = 5.09317122Subproblem 2
b + -2.9 = -2.19317122 Simplifying b + -2.9 = -2.19317122 Reorder the terms: -2.9 + b = -2.19317122 Solving -2.9 + b = -2.19317122 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + b = -2.19317122 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + b = -2.19317122 + 2.9 b = -2.19317122 + 2.9 Combine like terms: -2.19317122 + 2.9 = 0.70682878 b = 0.70682878 Simplifying b = 0.70682878Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.09317122, 0.70682878}
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