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Simplifying 8b2 + 16b + -14 = -3 Reorder the terms: -14 + 16b + 8b2 = -3 Solving -14 + 16b + 8b2 = -3 Solving for variable 'b'. Reorder the terms: -14 + 3 + 16b + 8b2 = -3 + 3 Combine like terms: -14 + 3 = -11 -11 + 16b + 8b2 = -3 + 3 Combine like terms: -3 + 3 = 0 -11 + 16b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 2b + b2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 2b + 1.375 + b2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 2b + b2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 2b + b2 = 0 + 1.375 2b + b2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 2b + b2 = 1.375 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 = 1.375 + 1 Reorder the terms: 1 + 2b + b2 = 1.375 + 1 Combine like terms: 1.375 + 1 = 2.375 1 + 2b + b2 = 2.375 Factor a perfect square on the left side: (b + 1)(b + 1) = 2.375 Calculate the square root of the right side: 1.541103501 Break this problem into two subproblems by setting (b + 1) equal to 1.541103501 and -1.541103501.Subproblem 1
b + 1 = 1.541103501 Simplifying b + 1 = 1.541103501 Reorder the terms: 1 + b = 1.541103501 Solving 1 + b = 1.541103501 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 = 1.541103501 + -1 Combine like terms: 1 + -1 = 0 0 + b = 1.541103501 + -1 b = 1.541103501 + -1 Combine like terms: 1.541103501 + -1 = 0.541103501 b = 0.541103501 Simplifying b = 0.541103501Subproblem 2
b + 1 = -1.541103501 Simplifying b + 1 = -1.541103501 Reorder the terms: 1 + b = -1.541103501 Solving 1 + b = -1.541103501 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 = -1.541103501 + -1 Combine like terms: 1 + -1 = 0 0 + b = -1.541103501 + -1 b = -1.541103501 + -1 Combine like terms: -1.541103501 + -1 = -2.541103501 b = -2.541103501 Simplifying b = -2.541103501Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.541103501, -2.541103501}
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