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Simplifying 3b2 + -18b = -14 Reorder the terms: -18b + 3b2 = -14 Solving -18b + 3b2 = -14 Solving for variable 'b'. Reorder the terms: 14 + -18b + 3b2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + -18b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + -6b + b2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -6b + -4.666666667 + b2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -6b + b2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -6b + b2 = 0 + -4.666666667 -6b + b2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -6b + b2 = -4.666666667 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = -4.666666667 + 9 Reorder the terms: 9 + -6b + b2 = -4.666666667 + 9 Combine like terms: -4.666666667 + 9 = 4.333333333 9 + -6b + b2 = 4.333333333 Factor a perfect square on the left side: (b + -3)(b + -3) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (b + -3) equal to 2.081665999 and -2.081665999.Subproblem 1
b + -3 = 2.081665999 Simplifying b + -3 = 2.081665999 Reorder the terms: -3 + b = 2.081665999 Solving -3 + b = 2.081665999 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + b = 2.081665999 + 3 b = 2.081665999 + 3 Combine like terms: 2.081665999 + 3 = 5.081665999 b = 5.081665999 Simplifying b = 5.081665999Subproblem 2
b + -3 = -2.081665999 Simplifying b + -3 = -2.081665999 Reorder the terms: -3 + b = -2.081665999 Solving -3 + b = -2.081665999 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + b = -2.081665999 + 3 b = -2.081665999 + 3 Combine like terms: -2.081665999 + 3 = 0.918334001 b = 0.918334001 Simplifying b = 0.918334001Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.081665999, 0.918334001}
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