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Simplifying b * b + 2b + -3 = 27 Multiply b * b b2 + 2b + -3 = 27 Reorder the terms: -3 + 2b + b2 = 27 Solving -3 + 2b + b2 = 27 Solving for variable 'b'. Reorder the terms: -3 + -27 + 2b + b2 = 27 + -27 Combine like terms: -3 + -27 = -30 -30 + 2b + b2 = 27 + -27 Combine like terms: 27 + -27 = 0 -30 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 2b + 30 + b2 = 0 + 30 Reorder the terms: -30 + 30 + 2b + b2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2b + b2 = 0 + 30 2b + b2 = 0 + 30 Combine like terms: 0 + 30 = 30 2b + b2 = 30 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 30 + 1 Reorder the terms: 1 + 2b + b2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2b + b2 = 31 Factor a perfect square on the left side: (b + 1)(b + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (b + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
b + 1 = 5.567764363 Simplifying b + 1 = 5.567764363 Reorder the terms: 1 + b = 5.567764363 Solving 1 + b = 5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + b = 5.567764363 + -1 b = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 b = 4.567764363 Simplifying b = 4.567764363Subproblem 2
b + 1 = -5.567764363 Simplifying b + 1 = -5.567764363 Reorder the terms: 1 + b = -5.567764363 Solving 1 + b = -5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + b = -5.567764363 + -1 b = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 b = -6.567764363 Simplifying b = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.567764363, -6.567764363}
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