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Simplifying b2 + 18b + -29 = 0 Reorder the terms: -29 + 18b + b2 = 0 Solving -29 + 18b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 18b + 29 + b2 = 0 + 29 Reorder the terms: -29 + 29 + 18b + b2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 18b + b2 = 0 + 29 18b + b2 = 0 + 29 Combine like terms: 0 + 29 = 29 18b + b2 = 29 The b term is 18b. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18b + 81 + b2 = 29 + 81 Reorder the terms: 81 + 18b + b2 = 29 + 81 Combine like terms: 29 + 81 = 110 81 + 18b + b2 = 110 Factor a perfect square on the left side: (b + 9)(b + 9) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (b + 9) equal to 10.488088482 and -10.488088482.Subproblem 1
b + 9 = 10.488088482 Simplifying b + 9 = 10.488088482 Reorder the terms: 9 + b = 10.488088482 Solving 9 + b = 10.488088482 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = 10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + b = 10.488088482 + -9 b = 10.488088482 + -9 Combine like terms: 10.488088482 + -9 = 1.488088482 b = 1.488088482 Simplifying b = 1.488088482Subproblem 2
b + 9 = -10.488088482 Simplifying b + 9 = -10.488088482 Reorder the terms: 9 + b = -10.488088482 Solving 9 + b = -10.488088482 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = -10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + b = -10.488088482 + -9 b = -10.488088482 + -9 Combine like terms: -10.488088482 + -9 = -19.488088482 b = -19.488088482 Simplifying b = -19.488088482Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.488088482, -19.488088482}
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