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Simplifying 3b2 + -6b + -16 = 0 Reorder the terms: -16 + -6b + 3b2 = 0 Solving -16 + -6b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -2b + b2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -2b + 5.333333333 + b2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -2b + b2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -2b + b2 = 0 + 5.333333333 -2b + b2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -2b + b2 = 5.333333333 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 = 5.333333333 + 1 Reorder the terms: 1 + -2b + b2 = 5.333333333 + 1 Combine like terms: 5.333333333 + 1 = 6.333333333 1 + -2b + b2 = 6.333333333 Factor a perfect square on the left side: (b + -1)(b + -1) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (b + -1) equal to 2.516611478 and -2.516611478.Subproblem 1
b + -1 = 2.516611478 Simplifying b + -1 = 2.516611478 Reorder the terms: -1 + b = 2.516611478 Solving -1 + b = 2.516611478 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 = 2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + b = 2.516611478 + 1 b = 2.516611478 + 1 Combine like terms: 2.516611478 + 1 = 3.516611478 b = 3.516611478 Simplifying b = 3.516611478Subproblem 2
b + -1 = -2.516611478 Simplifying b + -1 = -2.516611478 Reorder the terms: -1 + b = -2.516611478 Solving -1 + b = -2.516611478 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 = -2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + b = -2.516611478 + 1 b = -2.516611478 + 1 Combine like terms: -2.516611478 + 1 = -1.516611478 b = -1.516611478 Simplifying b = -1.516611478Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.516611478, -1.516611478}
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