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Simplifying b = -3b2 + 7b + 1 Reorder the terms: b = 1 + 7b + -3b2 Solving b = 1 + 7b + -3b2 Solving for variable 'b'. Reorder the terms: -1 + b + -7b + 3b2 = 1 + 7b + -3b2 + -1 + -7b + 3b2 Combine like terms: b + -7b = -6b -1 + -6b + 3b2 = 1 + 7b + -3b2 + -1 + -7b + 3b2 Reorder the terms: -1 + -6b + 3b2 = 1 + -1 + 7b + -7b + -3b2 + 3b2 Combine like terms: 1 + -1 = 0 -1 + -6b + 3b2 = 0 + 7b + -7b + -3b2 + 3b2 -1 + -6b + 3b2 = 7b + -7b + -3b2 + 3b2 Combine like terms: 7b + -7b = 0 -1 + -6b + 3b2 = 0 + -3b2 + 3b2 -1 + -6b + 3b2 = -3b2 + 3b2 Combine like terms: -3b2 + 3b2 = 0 -1 + -6b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -2b + b2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2b + 0.3333333333 + b2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2b + b2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2b + b2 = 0 + 0.3333333333 -2b + b2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2b + b2 = 0.3333333333 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 = 0.3333333333 + 1 Reorder the terms: 1 + -2b + b2 = 0.3333333333 + 1 Combine like terms: 0.3333333333 + 1 = 1.3333333333 1 + -2b + b2 = 1.3333333333 Factor a perfect square on the left side: (b + -1)(b + -1) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (b + -1) equal to 1.154700538 and -1.154700538.Subproblem 1
b + -1 = 1.154700538 Simplifying b + -1 = 1.154700538 Reorder the terms: -1 + b = 1.154700538 Solving -1 + b = 1.154700538 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 = 1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + b = 1.154700538 + 1 b = 1.154700538 + 1 Combine like terms: 1.154700538 + 1 = 2.154700538 b = 2.154700538 Simplifying b = 2.154700538Subproblem 2
b + -1 = -1.154700538 Simplifying b + -1 = -1.154700538 Reorder the terms: -1 + b = -1.154700538 Solving -1 + b = -1.154700538 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 = -1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + b = -1.154700538 + 1 b = -1.154700538 + 1 Combine like terms: -1.154700538 + 1 = -0.154700538 b = -0.154700538 Simplifying b = -0.154700538Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.154700538, -0.154700538}
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