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Simplifying (b2 + -7b + -44) + (b + 2) = 0 Reorder the terms: (-44 + -7b + b2) + (b + 2) = 0 Remove parenthesis around (-44 + -7b + b2) -44 + -7b + b2 + (b + 2) = 0 Reorder the terms: -44 + -7b + b2 + (2 + b) = 0 Remove parenthesis around (2 + b) -44 + -7b + b2 + 2 + b = 0 Reorder the terms: -44 + 2 + -7b + b + b2 = 0 Combine like terms: -44 + 2 = -42 -42 + -7b + b + b2 = 0 Combine like terms: -7b + b = -6b -42 + -6b + b2 = 0 Solving -42 + -6b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -6b + 42 + b2 = 0 + 42 Reorder the terms: -42 + 42 + -6b + b2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -6b + b2 = 0 + 42 -6b + b2 = 0 + 42 Combine like terms: 0 + 42 = 42 -6b + b2 = 42 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = 42 + 9 Reorder the terms: 9 + -6b + b2 = 42 + 9 Combine like terms: 42 + 9 = 51 9 + -6b + b2 = 51 Factor a perfect square on the left side: (b + -3)(b + -3) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (b + -3) equal to 7.141428429 and -7.141428429.Subproblem 1
b + -3 = 7.141428429 Simplifying b + -3 = 7.141428429 Reorder the terms: -3 + b = 7.141428429 Solving -3 + b = 7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 7.141428429 + 3 Combine like terms: -3 + 3 = 0 0 + b = 7.141428429 + 3 b = 7.141428429 + 3 Combine like terms: 7.141428429 + 3 = 10.141428429 b = 10.141428429 Simplifying b = 10.141428429Subproblem 2
b + -3 = -7.141428429 Simplifying b + -3 = -7.141428429 Reorder the terms: -3 + b = -7.141428429 Solving -3 + b = -7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -7.141428429 + 3 Combine like terms: -3 + 3 = 0 0 + b = -7.141428429 + 3 b = -7.141428429 + 3 Combine like terms: -7.141428429 + 3 = -4.141428429 b = -4.141428429 Simplifying b = -4.141428429Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.141428429, -4.141428429}
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