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Simplifying 15b2 + 18b + -35 = 0 Reorder the terms: -35 + 18b + 15b2 = 0 Solving -35 + 18b + 15b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.333333333 + 1.2b + b2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 1.2b + 2.333333333 + b2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 1.2b + b2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 1.2b + b2 = 0 + 2.333333333 1.2b + b2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 1.2b + b2 = 2.333333333 The b term is 1.2b. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2b + 0.36 + b2 = 2.333333333 + 0.36 Reorder the terms: 0.36 + 1.2b + b2 = 2.333333333 + 0.36 Combine like terms: 2.333333333 + 0.36 = 2.693333333 0.36 + 1.2b + b2 = 2.693333333 Factor a perfect square on the left side: (b + 0.6)(b + 0.6) = 2.693333333 Calculate the square root of the right side: 1.641137817 Break this problem into two subproblems by setting (b + 0.6) equal to 1.641137817 and -1.641137817.Subproblem 1
b + 0.6 = 1.641137817 Simplifying b + 0.6 = 1.641137817 Reorder the terms: 0.6 + b = 1.641137817 Solving 0.6 + b = 1.641137817 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + b = 1.641137817 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + b = 1.641137817 + -0.6 b = 1.641137817 + -0.6 Combine like terms: 1.641137817 + -0.6 = 1.041137817 b = 1.041137817 Simplifying b = 1.041137817Subproblem 2
b + 0.6 = -1.641137817 Simplifying b + 0.6 = -1.641137817 Reorder the terms: 0.6 + b = -1.641137817 Solving 0.6 + b = -1.641137817 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + b = -1.641137817 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + b = -1.641137817 + -0.6 b = -1.641137817 + -0.6 Combine like terms: -1.641137817 + -0.6 = -2.241137817 b = -2.241137817 Simplifying b = -2.241137817Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.041137817, -2.241137817}
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