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Simplifying b2 + 4b + -37 = -10 Reorder the terms: -37 + 4b + b2 = -10 Solving -37 + 4b + b2 = -10 Solving for variable 'b'. Reorder the terms: -37 + 10 + 4b + b2 = -10 + 10 Combine like terms: -37 + 10 = -27 -27 + 4b + b2 = -10 + 10 Combine like terms: -10 + 10 = 0 -27 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 4b + 27 + b2 = 0 + 27 Reorder the terms: -27 + 27 + 4b + b2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4b + b2 = 0 + 27 4b + b2 = 0 + 27 Combine like terms: 0 + 27 = 27 4b + b2 = 27 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = 27 + 4 Reorder the terms: 4 + 4b + b2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + 4b + b2 = 31 Factor a perfect square on the left side: (b + 2)(b + 2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (b + 2) equal to 5.567764363 and -5.567764363.Subproblem 1
b + 2 = 5.567764363 Simplifying b + 2 = 5.567764363 Reorder the terms: 2 + b = 5.567764363 Solving 2 + b = 5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + b = 5.567764363 + -2 b = 5.567764363 + -2 Combine like terms: 5.567764363 + -2 = 3.567764363 b = 3.567764363 Simplifying b = 3.567764363Subproblem 2
b + 2 = -5.567764363 Simplifying b + 2 = -5.567764363 Reorder the terms: 2 + b = -5.567764363 Solving 2 + b = -5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = -5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + b = -5.567764363 + -2 b = -5.567764363 + -2 Combine like terms: -5.567764363 + -2 = -7.567764363 b = -7.567764363 Simplifying b = -7.567764363Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.567764363, -7.567764363}
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