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Simplifying 10b + -45 = 3b(b + -15) Reorder the terms: -45 + 10b = 3b(b + -15) Reorder the terms: -45 + 10b = 3b(-15 + b) -45 + 10b = (-15 * 3b + b * 3b) -45 + 10b = (-45b + 3b2) Solving -45 + 10b = -45b + 3b2 Solving for variable 'b'. Combine like terms: 10b + 45b = 55b -45 + 55b + -3b2 = -45b + 3b2 + 45b + -3b2 Reorder the terms: -45 + 55b + -3b2 = -45b + 45b + 3b2 + -3b2 Combine like terms: -45b + 45b = 0 -45 + 55b + -3b2 = 0 + 3b2 + -3b2 -45 + 55b + -3b2 = 3b2 + -3b2 Combine like terms: 3b2 + -3b2 = 0 -45 + 55b + -3b2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 15 + -18.33333333b + b2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -18.33333333b + -15 + b2 = 0 + -15 Reorder the terms: 15 + -15 + -18.33333333b + b2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -18.33333333b + b2 = 0 + -15 -18.33333333b + b2 = 0 + -15 Combine like terms: 0 + -15 = -15 -18.33333333b + b2 = -15 The b term is -18.33333333b. Take half its coefficient (-9.166666665). Square it (84.02777775) and add it to both sides. Add '84.02777775' to each side of the equation. -18.33333333b + 84.02777775 + b2 = -15 + 84.02777775 Reorder the terms: 84.02777775 + -18.33333333b + b2 = -15 + 84.02777775 Combine like terms: -15 + 84.02777775 = 69.02777775 84.02777775 + -18.33333333b + b2 = 69.02777775 Factor a perfect square on the left side: (b + -9.166666665)(b + -9.166666665) = 69.02777775 Calculate the square root of the right side: 8.308295719 Break this problem into two subproblems by setting (b + -9.166666665) equal to 8.308295719 and -8.308295719.Subproblem 1
b + -9.166666665 = 8.308295719 Simplifying b + -9.166666665 = 8.308295719 Reorder the terms: -9.166666665 + b = 8.308295719 Solving -9.166666665 + b = 8.308295719 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9.166666665' to each side of the equation. -9.166666665 + 9.166666665 + b = 8.308295719 + 9.166666665 Combine like terms: -9.166666665 + 9.166666665 = 0.000000000 0.000000000 + b = 8.308295719 + 9.166666665 b = 8.308295719 + 9.166666665 Combine like terms: 8.308295719 + 9.166666665 = 17.474962384 b = 17.474962384 Simplifying b = 17.474962384Subproblem 2
b + -9.166666665 = -8.308295719 Simplifying b + -9.166666665 = -8.308295719 Reorder the terms: -9.166666665 + b = -8.308295719 Solving -9.166666665 + b = -8.308295719 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9.166666665' to each side of the equation. -9.166666665 + 9.166666665 + b = -8.308295719 + 9.166666665 Combine like terms: -9.166666665 + 9.166666665 = 0.000000000 0.000000000 + b = -8.308295719 + 9.166666665 b = -8.308295719 + 9.166666665 Combine like terms: -8.308295719 + 9.166666665 = 0.858370946 b = 0.858370946 Simplifying b = 0.858370946Solution
The solution to the problem is based on the solutions from the subproblems. b = {17.474962384, 0.858370946}
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