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Simplifying b2 + 5 + -8b + -10 = 0 Reorder the terms: 5 + -10 + -8b + b2 = 0 Combine like terms: 5 + -10 = -5 -5 + -8b + b2 = 0 Solving -5 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -8b + 5 + b2 = 0 + 5 Reorder the terms: -5 + 5 + -8b + b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8b + b2 = 0 + 5 -8b + b2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8b + b2 = 5 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 = 5 + 16 Reorder the terms: 16 + -8b + b2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + -8b + b2 = 21 Factor a perfect square on the left side: (b + -4)(b + -4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (b + -4) equal to 4.582575695 and -4.582575695.Subproblem 1
b + -4 = 4.582575695 Simplifying b + -4 = 4.582575695 Reorder the terms: -4 + b = 4.582575695 Solving -4 + b = 4.582575695 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 = 4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + b = 4.582575695 + 4 b = 4.582575695 + 4 Combine like terms: 4.582575695 + 4 = 8.582575695 b = 8.582575695 Simplifying b = 8.582575695Subproblem 2
b + -4 = -4.582575695 Simplifying b + -4 = -4.582575695 Reorder the terms: -4 + b = -4.582575695 Solving -4 + b = -4.582575695 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 = -4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + b = -4.582575695 + 4 b = -4.582575695 + 4 Combine like terms: -4.582575695 + 4 = -0.582575695 b = -0.582575695 Simplifying b = -0.582575695Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.582575695, -0.582575695}
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