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Simplifying b2 + 5b + -35 = 3 Reorder the terms: -35 + 5b + b2 = 3 Solving -35 + 5b + b2 = 3 Solving for variable 'b'. Reorder the terms: -35 + -3 + 5b + b2 = 3 + -3 Combine like terms: -35 + -3 = -38 -38 + 5b + b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -38 + 5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 5b + 38 + b2 = 0 + 38 Reorder the terms: -38 + 38 + 5b + b2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 5b + b2 = 0 + 38 5b + b2 = 0 + 38 Combine like terms: 0 + 38 = 38 5b + b2 = 38 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = 38 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 38 + 6.25 Combine like terms: 38 + 6.25 = 44.25 6.25 + 5b + b2 = 44.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (b + 2.5) equal to 6.652067348 and -6.652067348.Subproblem 1
b + 2.5 = 6.652067348 Simplifying b + 2.5 = 6.652067348 Reorder the terms: 2.5 + b = 6.652067348 Solving 2.5 + b = 6.652067348 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 6.652067348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 6.652067348 + -2.5 b = 6.652067348 + -2.5 Combine like terms: 6.652067348 + -2.5 = 4.152067348 b = 4.152067348 Simplifying b = 4.152067348Subproblem 2
b + 2.5 = -6.652067348 Simplifying b + 2.5 = -6.652067348 Reorder the terms: 2.5 + b = -6.652067348 Solving 2.5 + b = -6.652067348 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -6.652067348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -6.652067348 + -2.5 b = -6.652067348 + -2.5 Combine like terms: -6.652067348 + -2.5 = -9.152067348 b = -9.152067348 Simplifying b = -9.152067348Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.152067348, -9.152067348}
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