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Simplifying 3b(6 + -1b) = -22 (6 * 3b + -1b * 3b) = -22 (18b + -3b2) = -22 Solving 18b + -3b2 = -22 Solving for variable 'b'. Reorder the terms: 22 + 18b + -3b2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 18b + -3b2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.333333333 + -6b + b2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -6b + 7.333333333 + b2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -6b + b2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -6b + b2 = 0 + 7.333333333 -6b + b2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -6b + b2 = 7.333333333 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 = 7.333333333 + 9 Reorder the terms: 9 + -6b + b2 = 7.333333333 + 9 Combine like terms: 7.333333333 + 9 = 16.333333333 9 + -6b + b2 = 16.333333333 Factor a perfect square on the left side: (b + -3)(b + -3) = 16.333333333 Calculate the square root of the right side: 4.041451884 Break this problem into two subproblems by setting (b + -3) equal to 4.041451884 and -4.041451884.Subproblem 1
b + -3 = 4.041451884 Simplifying b + -3 = 4.041451884 Reorder the terms: -3 + b = 4.041451884 Solving -3 + b = 4.041451884 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 = 4.041451884 + 3 Combine like terms: -3 + 3 = 0 0 + b = 4.041451884 + 3 b = 4.041451884 + 3 Combine like terms: 4.041451884 + 3 = 7.041451884 b = 7.041451884 Simplifying b = 7.041451884Subproblem 2
b + -3 = -4.041451884 Simplifying b + -3 = -4.041451884 Reorder the terms: -3 + b = -4.041451884 Solving -3 + b = -4.041451884 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 = -4.041451884 + 3 Combine like terms: -3 + 3 = 0 0 + b = -4.041451884 + 3 b = -4.041451884 + 3 Combine like terms: -4.041451884 + 3 = -1.041451884 b = -1.041451884 Simplifying b = -1.041451884Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.041451884, -1.041451884}
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