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Simplifying b2 + 8b + -15 = 0 Reorder the terms: -15 + 8b + b2 = 0 Solving -15 + 8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 8b + 15 + b2 = 0 + 15 Reorder the terms: -15 + 15 + 8b + b2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8b + b2 = 0 + 15 8b + b2 = 0 + 15 Combine like terms: 0 + 15 = 15 8b + b2 = 15 The b term is 8b. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8b + 16 + b2 = 15 + 16 Reorder the terms: 16 + 8b + b2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + 8b + b2 = 31 Factor a perfect square on the left side: (b + 4)(b + 4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (b + 4) equal to 5.567764363 and -5.567764363.Subproblem 1
b + 4 = 5.567764363 Simplifying b + 4 = 5.567764363 Reorder the terms: 4 + b = 5.567764363 Solving 4 + b = 5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + b = 5.567764363 + -4 b = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 b = 1.567764363 Simplifying b = 1.567764363Subproblem 2
b + 4 = -5.567764363 Simplifying b + 4 = -5.567764363 Reorder the terms: 4 + b = -5.567764363 Solving 4 + b = -5.567764363 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + b = -5.567764363 + -4 b = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 b = -9.567764363 Simplifying b = -9.567764363Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.567764363, -9.567764363}
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