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Simplifying 9b(b + -2) = 156 Reorder the terms: 9b(-2 + b) = 156 (-2 * 9b + b * 9b) = 156 (-18b + 9b2) = 156 Solving -18b + 9b2 = 156 Solving for variable 'b'. Reorder the terms: -156 + -18b + 9b2 = 156 + -156 Combine like terms: 156 + -156 = 0 -156 + -18b + 9b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-52 + -6b + 3b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-52 + -6b + 3b2)' equal to zero and attempt to solve: Simplifying -52 + -6b + 3b2 = 0 Solving -52 + -6b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17.33333333 + -2b + b2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + -2b + 17.33333333 + b2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + -2b + b2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + -2b + b2 = 0 + 17.33333333 -2b + b2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 -2b + b2 = 17.33333333 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 17.33333333 + 1 Reorder the terms: 1 + -2b + b2 = 17.33333333 + 1 Combine like terms: 17.33333333 + 1 = 18.33333333 1 + -2b + b2 = 18.33333333 Factor a perfect square on the left side: (b + -1)(b + -1) = 18.33333333 Calculate the square root of the right side: 4.281744192 Break this problem into two subproblems by setting (b + -1) equal to 4.281744192 and -4.281744192.Subproblem 1
b + -1 = 4.281744192 Simplifying b + -1 = 4.281744192 Reorder the terms: -1 + b = 4.281744192 Solving -1 + b = 4.281744192 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 4.281744192 + 1 Combine like terms: -1 + 1 = 0 0 + b = 4.281744192 + 1 b = 4.281744192 + 1 Combine like terms: 4.281744192 + 1 = 5.281744192 b = 5.281744192 Simplifying b = 5.281744192Subproblem 2
b + -1 = -4.281744192 Simplifying b + -1 = -4.281744192 Reorder the terms: -1 + b = -4.281744192 Solving -1 + b = -4.281744192 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -4.281744192 + 1 Combine like terms: -1 + 1 = 0 0 + b = -4.281744192 + 1 b = -4.281744192 + 1 Combine like terms: -4.281744192 + 1 = -3.281744192 b = -3.281744192 Simplifying b = -3.281744192Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.281744192, -3.281744192}Solution
b = {5.281744192, -3.281744192}
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