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Simplifying 4b2 + 3b + -25 = 0 Reorder the terms: -25 + 3b + 4b2 = 0 Solving -25 + 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'. -6.25 + 0.75b + b2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.75b + 6.25 + b2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.75b + b2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.75b + b2 = 0 + 6.25 0.75b + b2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.75b + b2 = 6.25 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 = 6.25 + 0.140625 Reorder the terms: 0.140625 + 0.75b + b2 = 6.25 + 0.140625 Combine like terms: 6.25 + 0.140625 = 6.390625 0.140625 + 0.75b + b2 = 6.390625 Factor a perfect square on the left side: (b + 0.375)(b + 0.375) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (b + 0.375) equal to 2.527968552 and -2.527968552.Subproblem 1
b + 0.375 = 2.527968552 Simplifying b + 0.375 = 2.527968552 Reorder the terms: 0.375 + b = 2.527968552 Solving 0.375 + b = 2.527968552 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 = 2.527968552 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + b = 2.527968552 + -0.375 b = 2.527968552 + -0.375 Combine like terms: 2.527968552 + -0.375 = 2.152968552 b = 2.152968552 Simplifying b = 2.152968552Subproblem 2
b + 0.375 = -2.527968552 Simplifying b + 0.375 = -2.527968552 Reorder the terms: 0.375 + b = -2.527968552 Solving 0.375 + b = -2.527968552 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 = -2.527968552 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + b = -2.527968552 + -0.375 b = -2.527968552 + -0.375 Combine like terms: -2.527968552 + -0.375 = -2.902968552 b = -2.902968552 Simplifying b = -2.902968552Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.152968552, -2.902968552}
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