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Simplifying b2 + -12b + 25 = 0 Reorder the terms: 25 + -12b + b2 = 0 Solving 25 + -12b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12b + -25 + b2 = 0 + -25 Reorder the terms: 25 + -25 + -12b + b2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12b + b2 = 0 + -25 -12b + b2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12b + b2 = -25 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 = -25 + 36 Reorder the terms: 36 + -12b + b2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + -12b + b2 = 11 Factor a perfect square on the left side: (b + -6)(b + -6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + -6) equal to 3.31662479 and -3.31662479.Subproblem 1
b + -6 = 3.31662479 Simplifying b + -6 = 3.31662479 Reorder the terms: -6 + b = 3.31662479 Solving -6 + b = 3.31662479 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 = 3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + b = 3.31662479 + 6 b = 3.31662479 + 6 Combine like terms: 3.31662479 + 6 = 9.31662479 b = 9.31662479 Simplifying b = 9.31662479Subproblem 2
b + -6 = -3.31662479 Simplifying b + -6 = -3.31662479 Reorder the terms: -6 + b = -3.31662479 Solving -6 + b = -3.31662479 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 = -3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + b = -3.31662479 + 6 b = -3.31662479 + 6 Combine like terms: -3.31662479 + 6 = 2.68337521 b = 2.68337521 Simplifying b = 2.68337521Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.31662479, 2.68337521}
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