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Simplifying b2 + -16b + 64 = 14 Reorder the terms: 64 + -16b + b2 = 14 Solving 64 + -16b + b2 = 14 Solving for variable 'b'. Reorder the terms: 64 + -14 + -16b + b2 = 14 + -14 Combine like terms: 64 + -14 = 50 50 + -16b + b2 = 14 + -14 Combine like terms: 14 + -14 = 0 50 + -16b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -16b + -50 + b2 = 0 + -50 Reorder the terms: 50 + -50 + -16b + b2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -16b + b2 = 0 + -50 -16b + b2 = 0 + -50 Combine like terms: 0 + -50 = -50 -16b + b2 = -50 The b term is -16b. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16b + 64 + b2 = -50 + 64 Reorder the terms: 64 + -16b + b2 = -50 + 64 Combine like terms: -50 + 64 = 14 64 + -16b + b2 = 14 Factor a perfect square on the left side: (b + -8)(b + -8) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (b + -8) equal to 3.741657387 and -3.741657387.Subproblem 1
b + -8 = 3.741657387 Simplifying b + -8 = 3.741657387 Reorder the terms: -8 + b = 3.741657387 Solving -8 + b = 3.741657387 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = 3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + b = 3.741657387 + 8 b = 3.741657387 + 8 Combine like terms: 3.741657387 + 8 = 11.741657387 b = 11.741657387 Simplifying b = 11.741657387Subproblem 2
b + -8 = -3.741657387 Simplifying b + -8 = -3.741657387 Reorder the terms: -8 + b = -3.741657387 Solving -8 + b = -3.741657387 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = -3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + b = -3.741657387 + 8 b = -3.741657387 + 8 Combine like terms: -3.741657387 + 8 = 4.258342613 b = 4.258342613 Simplifying b = 4.258342613Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.741657387, 4.258342613}
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