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Simplifying b2 + 12b + -86 = 10 Reorder the terms: -86 + 12b + b2 = 10 Solving -86 + 12b + b2 = 10 Solving for variable 'b'. Reorder the terms: -86 + -10 + 12b + b2 = 10 + -10 Combine like terms: -86 + -10 = -96 -96 + 12b + b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -96 + 12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 12b + 96 + b2 = 0 + 96 Reorder the terms: -96 + 96 + 12b + b2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 12b + b2 = 0 + 96 12b + b2 = 0 + 96 Combine like terms: 0 + 96 = 96 12b + b2 = 96 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 = 96 + 36 Reorder the terms: 36 + 12b + b2 = 96 + 36 Combine like terms: 96 + 36 = 132 36 + 12b + b2 = 132 Factor a perfect square on the left side: (b + 6)(b + 6) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (b + 6) equal to 11.489125293 and -11.489125293.Subproblem 1
b + 6 = 11.489125293 Simplifying b + 6 = 11.489125293 Reorder the terms: 6 + b = 11.489125293 Solving 6 + b = 11.489125293 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 = 11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + b = 11.489125293 + -6 b = 11.489125293 + -6 Combine like terms: 11.489125293 + -6 = 5.489125293 b = 5.489125293 Simplifying b = 5.489125293Subproblem 2
b + 6 = -11.489125293 Simplifying b + 6 = -11.489125293 Reorder the terms: 6 + b = -11.489125293 Solving 6 + b = -11.489125293 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 = -11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + b = -11.489125293 + -6 b = -11.489125293 + -6 Combine like terms: -11.489125293 + -6 = -17.489125293 b = -17.489125293 Simplifying b = -17.489125293Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.489125293, -17.489125293}
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