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Simplifying 3b2 + -18b + 5 = 15 Reorder the terms: 5 + -18b + 3b2 = 15 Solving 5 + -18b + 3b2 = 15 Solving for variable 'b'. Reorder the terms: 5 + -15 + -18b + 3b2 = 15 + -15 Combine like terms: 5 + -15 = -10 -10 + -18b + 3b2 = 15 + -15 Combine like terms: 15 + -15 = 0 -10 + -18b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -6b + b2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -6b + 3.333333333 + b2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -6b + b2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -6b + b2 = 0 + 3.333333333 -6b + b2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -6b + b2 = 3.333333333 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 = 3.333333333 + 9 Reorder the terms: 9 + -6b + b2 = 3.333333333 + 9 Combine like terms: 3.333333333 + 9 = 12.333333333 9 + -6b + b2 = 12.333333333 Factor a perfect square on the left side: (b + -3)(b + -3) = 12.333333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (b + -3) equal to 3.511884584 and -3.511884584.Subproblem 1
b + -3 = 3.511884584 Simplifying b + -3 = 3.511884584 Reorder the terms: -3 + b = 3.511884584 Solving -3 + b = 3.511884584 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 = 3.511884584 + 3 Combine like terms: -3 + 3 = 0 0 + b = 3.511884584 + 3 b = 3.511884584 + 3 Combine like terms: 3.511884584 + 3 = 6.511884584 b = 6.511884584 Simplifying b = 6.511884584Subproblem 2
b + -3 = -3.511884584 Simplifying b + -3 = -3.511884584 Reorder the terms: -3 + b = -3.511884584 Solving -3 + b = -3.511884584 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 = -3.511884584 + 3 Combine like terms: -3 + 3 = 0 0 + b = -3.511884584 + 3 b = -3.511884584 + 3 Combine like terms: -3.511884584 + 3 = -0.511884584 b = -0.511884584 Simplifying b = -0.511884584Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.511884584, -0.511884584}
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