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Simplifying (4b2) + -1b + -96 = 0 Reorder the terms: -96 + -1b + (4b2) = 0 Solving -96 + -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'. -24 + -0.25b + b2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -0.25b + 24 + b2 = 0 + 24 Reorder the terms: -24 + 24 + -0.25b + b2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -0.25b + b2 = 0 + 24 -0.25b + b2 = 0 + 24 Combine like terms: 0 + 24 = 24 -0.25b + b2 = 24 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 = 24 + 0.015625 Reorder the terms: 0.015625 + -0.25b + b2 = 24 + 0.015625 Combine like terms: 24 + 0.015625 = 24.015625 0.015625 + -0.25b + b2 = 24.015625 Factor a perfect square on the left side: ((b) + -0.125)((b) + -0.125) = 24.015625 Calculate the square root of the right side: 4.900573946 Break this problem into two subproblems by setting ((b) + -0.125) equal to 4.900573946 and -4.900573946.Subproblem 1
(b) + -0.125 = 4.900573946 Simplifying (b) + -0.125 = 4.900573946 b + -0.125 = 4.900573946 Reorder the terms: -0.125 + b = 4.900573946 Solving -0.125 + b = 4.900573946 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 = 4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = 4.900573946 + 0.125 b = 4.900573946 + 0.125 Combine like terms: 4.900573946 + 0.125 = 5.025573946 b = 5.025573946 Simplifying b = 5.025573946Subproblem 2
(b) + -0.125 = -4.900573946 Simplifying (b) + -0.125 = -4.900573946 b + -0.125 = -4.900573946 Reorder the terms: -0.125 + b = -4.900573946 Solving -0.125 + b = -4.900573946 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 = -4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = -4.900573946 + 0.125 b = -4.900573946 + 0.125 Combine like terms: -4.900573946 + 0.125 = -4.775573946 b = -4.775573946 Simplifying b = -4.775573946Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.025573946, -4.775573946}
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