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Simplifying b2 + 2b + 1 = 7b + -2 Reorder the terms: 1 + 2b + b2 = 7b + -2 Reorder the terms: 1 + 2b + b2 = -2 + 7b Solving 1 + 2b + b2 = -2 + 7b Solving for variable 'b'. Reorder the terms: 1 + 2 + 2b + -7b + b2 = -2 + 7b + 2 + -7b Combine like terms: 1 + 2 = 3 3 + 2b + -7b + b2 = -2 + 7b + 2 + -7b Combine like terms: 2b + -7b = -5b 3 + -5b + b2 = -2 + 7b + 2 + -7b Reorder the terms: 3 + -5b + b2 = -2 + 2 + 7b + -7b Combine like terms: -2 + 2 = 0 3 + -5b + b2 = 0 + 7b + -7b 3 + -5b + b2 = 7b + -7b Combine like terms: 7b + -7b = 0 3 + -5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5b + -3 + b2 = 0 + -3 Reorder the terms: 3 + -3 + -5b + b2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b + b2 = 0 + -3 -5b + b2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5b + b2 = -3 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = -3 + 6.25 Reorder the terms: 6.25 + -5b + b2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5b + b2 = 3.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (b + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
b + -2.5 = 1.802775638 Simplifying b + -2.5 = 1.802775638 Reorder the terms: -2.5 + b = 1.802775638 Solving -2.5 + b = 1.802775638 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 1.802775638 + 2.5 b = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 b = 4.302775638 Simplifying b = 4.302775638Subproblem 2
b + -2.5 = -1.802775638 Simplifying b + -2.5 = -1.802775638 Reorder the terms: -2.5 + b = -1.802775638 Solving -2.5 + b = -1.802775638 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -1.802775638 + 2.5 b = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 b = 0.697224362 Simplifying b = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.302775638, 0.697224362}
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