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Simplifying 4b2 + -3b + -8 = 0 Reorder the terms: -8 + -3b + 4b2 = 0 Solving -8 + -3b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -0.75b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.75b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -0.75b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.75b + b2 = 0 + 2 -0.75b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.75b + b2 = 2 The b term is -0.75b. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75b + 0.140625 + b2 = 2 + 0.140625 Reorder the terms: 0.140625 + -0.75b + b2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + -0.75b + b2 = 2.140625 Factor a perfect square on the left side: (b + -0.375)(b + -0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (b + -0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
b + -0.375 = 1.463087489 Simplifying b + -0.375 = 1.463087489 Reorder the terms: -0.375 + b = 1.463087489 Solving -0.375 + b = 1.463087489 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + b = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + b = 1.463087489 + 0.375 b = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 b = 1.838087489 Simplifying b = 1.838087489Subproblem 2
b + -0.375 = -1.463087489 Simplifying b + -0.375 = -1.463087489 Reorder the terms: -0.375 + b = -1.463087489 Solving -0.375 + b = -1.463087489 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + b = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + b = -1.463087489 + 0.375 b = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 b = -1.088087489 Simplifying b = -1.088087489Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.838087489, -1.088087489}
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