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Simplifying 4b2 + -1b + -8 = 0 Reorder the terms: -8 + -1b + 4b2 = 0 Solving -8 + -1b + 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 + -0.25b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.25b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -0.25b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.25b + b2 = 0 + 2 -0.25b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.25b + b2 = 2 The b term is -0.25b. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25b + 0.015625 + b2 = 2 + 0.015625 Reorder the terms: 0.015625 + -0.25b + b2 = 2 + 0.015625 Combine like terms: 2 + 0.015625 = 2.015625 0.015625 + -0.25b + b2 = 2.015625 Factor a perfect square on the left side: (b + -0.125)(b + -0.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (b + -0.125) equal to 1.419727086 and -1.419727086.Subproblem 1
b + -0.125 = 1.419727086 Simplifying b + -0.125 = 1.419727086 Reorder the terms: -0.125 + b = 1.419727086 Solving -0.125 + b = 1.419727086 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = 1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = 1.419727086 + 0.125 b = 1.419727086 + 0.125 Combine like terms: 1.419727086 + 0.125 = 1.544727086 b = 1.544727086 Simplifying b = 1.544727086Subproblem 2
b + -0.125 = -1.419727086 Simplifying b + -0.125 = -1.419727086 Reorder the terms: -0.125 + b = -1.419727086 Solving -0.125 + b = -1.419727086 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = -1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = -1.419727086 + 0.125 b = -1.419727086 + 0.125 Combine like terms: -1.419727086 + 0.125 = -1.294727086 b = -1.294727086 Simplifying b = -1.294727086Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.544727086, -1.294727086}
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