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Simplifying b2 + -12b + 9 = 0 Reorder the terms: 9 + -12b + b2 = 0 Solving 9 + -12b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -12b + -9 + b2 = 0 + -9 Reorder the terms: 9 + -9 + -12b + b2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -12b + b2 = 0 + -9 -12b + b2 = 0 + -9 Combine like terms: 0 + -9 = -9 -12b + b2 = -9 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = -9 + 36 Reorder the terms: 36 + -12b + b2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + -12b + b2 = 27 Factor a perfect square on the left side: (b + -6)(b + -6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (b + -6) equal to 5.196152423 and -5.196152423.Subproblem 1
b + -6 = 5.196152423 Simplifying b + -6 = 5.196152423 Reorder the terms: -6 + b = 5.196152423 Solving -6 + b = 5.196152423 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + b = 5.196152423 + 6 b = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 b = 11.196152423 Simplifying b = 11.196152423Subproblem 2
b + -6 = -5.196152423 Simplifying b + -6 = -5.196152423 Reorder the terms: -6 + b = -5.196152423 Solving -6 + b = -5.196152423 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + b = -5.196152423 + 6 b = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 b = 0.803847577 Simplifying b = 0.803847577Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.196152423, 0.803847577}
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