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Simplifying -8b2 + -2b = -16 Reorder the terms: -2b + -8b2 = -16 Solving -2b + -8b2 = -16 Solving for variable 'b'. Reorder the terms: 16 + -2b + -8b2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -2b + -8b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -1b + -4b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1b + -4b2)' equal to zero and attempt to solve: Simplifying 8 + -1b + -4b2 = 0 Solving 8 + -1b + -4b2 = 0 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 = 1.294727086 b = 1.294727086 Simplifying b = 1.294727086Subproblem 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 = -1.544727086 b = -1.544727086 Simplifying b = -1.544727086Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.294727086, -1.544727086}Solution
b = {1.294727086, -1.544727086}
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