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Simplifying 15 + -1(8 + b) * b = -9 Reorder the terms for easier multiplication: 15 + -1b(8 + b) = -9 15 + (8 * -1b + b * -1b) = -9 15 + (-8b + -1b2) = -9 Solving 15 + -8b + -1b2 = -9 Solving for variable 'b'. Reorder the terms: 15 + 9 + -8b + -1b2 = -9 + 9 Combine like terms: 15 + 9 = 24 24 + -8b + -1b2 = -9 + 9 Combine like terms: -9 + 9 = 0 24 + -8b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 8b + b2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 8b + 24 + b2 = 0 + 24 Reorder the terms: -24 + 24 + 8b + b2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 8b + b2 = 0 + 24 8b + b2 = 0 + 24 Combine like terms: 0 + 24 = 24 8b + b2 = 24 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 = 24 + 16 Reorder the terms: 16 + 8b + b2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + 8b + b2 = 40 Factor a perfect square on the left side: (b + 4)(b + 4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (b + 4) equal to 6.32455532 and -6.32455532.Subproblem 1
b + 4 = 6.32455532 Simplifying b + 4 = 6.32455532 Reorder the terms: 4 + b = 6.32455532 Solving 4 + b = 6.32455532 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 = 6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + b = 6.32455532 + -4 b = 6.32455532 + -4 Combine like terms: 6.32455532 + -4 = 2.32455532 b = 2.32455532 Simplifying b = 2.32455532Subproblem 2
b + 4 = -6.32455532 Simplifying b + 4 = -6.32455532 Reorder the terms: 4 + b = -6.32455532 Solving 4 + b = -6.32455532 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 = -6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + b = -6.32455532 + -4 b = -6.32455532 + -4 Combine like terms: -6.32455532 + -4 = -10.32455532 b = -10.32455532 Simplifying b = -10.32455532Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.32455532, -10.32455532}
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