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Simplifying 8b2 + -5b + -19 = 0 Reorder the terms: -19 + -5b + 8b2 = 0 Solving -19 + -5b + 8b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + -0.625b + b2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -0.625b + 2.375 + b2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -0.625b + b2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -0.625b + b2 = 0 + 2.375 -0.625b + b2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -0.625b + b2 = 2.375 The b term is -0.625b. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625b + 0.09765625 + b2 = 2.375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625b + b2 = 2.375 + 0.09765625 Combine like terms: 2.375 + 0.09765625 = 2.47265625 0.09765625 + -0.625b + b2 = 2.47265625 Factor a perfect square on the left side: (b + -0.3125)(b + -0.3125) = 2.47265625 Calculate the square root of the right side: 1.572468203 Break this problem into two subproblems by setting (b + -0.3125) equal to 1.572468203 and -1.572468203.Subproblem 1
b + -0.3125 = 1.572468203 Simplifying b + -0.3125 = 1.572468203 Reorder the terms: -0.3125 + b = 1.572468203 Solving -0.3125 + b = 1.572468203 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + b = 1.572468203 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + b = 1.572468203 + 0.3125 b = 1.572468203 + 0.3125 Combine like terms: 1.572468203 + 0.3125 = 1.884968203 b = 1.884968203 Simplifying b = 1.884968203Subproblem 2
b + -0.3125 = -1.572468203 Simplifying b + -0.3125 = -1.572468203 Reorder the terms: -0.3125 + b = -1.572468203 Solving -0.3125 + b = -1.572468203 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + b = -1.572468203 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + b = -1.572468203 + 0.3125 b = -1.572468203 + 0.3125 Combine like terms: -1.572468203 + 0.3125 = -1.259968203 b = -1.259968203 Simplifying b = -1.259968203Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.884968203, -1.259968203}
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