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Simplifying 3b2 + -61b + 12 = 0 Reorder the terms: 12 + -61b + 3b2 = 0 Solving 12 + -61b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -20.33333333b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -20.33333333b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -20.33333333b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -20.33333333b + b2 = 0 + -4 -20.33333333b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -20.33333333b + b2 = -4 The b term is -20.33333333b. Take half its coefficient (-10.16666667). Square it (103.3611112) and add it to both sides. Add '103.3611112' to each side of the equation. -20.33333333b + 103.3611112 + b2 = -4 + 103.3611112 Reorder the terms: 103.3611112 + -20.33333333b + b2 = -4 + 103.3611112 Combine like terms: -4 + 103.3611112 = 99.3611112 103.3611112 + -20.33333333b + b2 = 99.3611112 Factor a perfect square on the left side: (b + -10.16666667)(b + -10.16666667) = 99.3611112 Calculate the square root of the right side: 9.968004374 Break this problem into two subproblems by setting (b + -10.16666667) equal to 9.968004374 and -9.968004374.Subproblem 1
b + -10.16666667 = 9.968004374 Simplifying b + -10.16666667 = 9.968004374 Reorder the terms: -10.16666667 + b = 9.968004374 Solving -10.16666667 + b = 9.968004374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10.16666667' to each side of the equation. -10.16666667 + 10.16666667 + b = 9.968004374 + 10.16666667 Combine like terms: -10.16666667 + 10.16666667 = 0.00000000 0.00000000 + b = 9.968004374 + 10.16666667 b = 9.968004374 + 10.16666667 Combine like terms: 9.968004374 + 10.16666667 = 20.134671044 b = 20.134671044 Simplifying b = 20.134671044Subproblem 2
b + -10.16666667 = -9.968004374 Simplifying b + -10.16666667 = -9.968004374 Reorder the terms: -10.16666667 + b = -9.968004374 Solving -10.16666667 + b = -9.968004374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10.16666667' to each side of the equation. -10.16666667 + 10.16666667 + b = -9.968004374 + 10.16666667 Combine like terms: -10.16666667 + 10.16666667 = 0.00000000 0.00000000 + b = -9.968004374 + 10.16666667 b = -9.968004374 + 10.16666667 Combine like terms: -9.968004374 + 10.16666667 = 0.198662296 b = 0.198662296 Simplifying b = 0.198662296Solution
The solution to the problem is based on the solutions from the subproblems. b = {20.134671044, 0.198662296}
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