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Simplifying b2 + -8b + 16 = 12 Reorder the terms: 16 + -8b + b2 = 12 Solving 16 + -8b + b2 = 12 Solving for variable 'b'. Reorder the terms: 16 + -12 + -8b + b2 = 12 + -12 Combine like terms: 16 + -12 = 4 4 + -8b + b2 = 12 + -12 Combine like terms: 12 + -12 = 0 4 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -8b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8b + b2 = 0 + -4 -8b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8b + b2 = -4 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 = -4 + 16 Reorder the terms: 16 + -8b + b2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8b + b2 = 12 Factor a perfect square on the left side: (b + -4)(b + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (b + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
b + -4 = 3.464101615 Simplifying b + -4 = 3.464101615 Reorder the terms: -4 + b = 3.464101615 Solving -4 + b = 3.464101615 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 = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + b = 3.464101615 + 4 b = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 b = 7.464101615 Simplifying b = 7.464101615Subproblem 2
b + -4 = -3.464101615 Simplifying b + -4 = -3.464101615 Reorder the terms: -4 + b = -3.464101615 Solving -4 + b = -3.464101615 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 = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + b = -3.464101615 + 4 b = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 b = 0.535898385 Simplifying b = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.464101615, 0.535898385}
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