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Simplifying b2 + 8b + -57 = 6 Reorder the terms: -57 + 8b + b2 = 6 Solving -57 + 8b + b2 = 6 Solving for variable 'b'. Reorder the terms: -57 + -6 + 8b + b2 = 6 + -6 Combine like terms: -57 + -6 = -63 -63 + 8b + b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -63 + 8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 8b + 63 + b2 = 0 + 63 Reorder the terms: -63 + 63 + 8b + b2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 8b + b2 = 0 + 63 8b + b2 = 0 + 63 Combine like terms: 0 + 63 = 63 8b + b2 = 63 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 = 63 + 16 Reorder the terms: 16 + 8b + b2 = 63 + 16 Combine like terms: 63 + 16 = 79 16 + 8b + b2 = 79 Factor a perfect square on the left side: (b + 4)(b + 4) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (b + 4) equal to 8.888194417 and -8.888194417.Subproblem 1
b + 4 = 8.888194417 Simplifying b + 4 = 8.888194417 Reorder the terms: 4 + b = 8.888194417 Solving 4 + b = 8.888194417 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 = 8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + b = 8.888194417 + -4 b = 8.888194417 + -4 Combine like terms: 8.888194417 + -4 = 4.888194417 b = 4.888194417 Simplifying b = 4.888194417Subproblem 2
b + 4 = -8.888194417 Simplifying b + 4 = -8.888194417 Reorder the terms: 4 + b = -8.888194417 Solving 4 + b = -8.888194417 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 = -8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + b = -8.888194417 + -4 b = -8.888194417 + -4 Combine like terms: -8.888194417 + -4 = -12.888194417 b = -12.888194417 Simplifying b = -12.888194417Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.888194417, -12.888194417}
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