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Simplifying b2 + 2b + -35 = 3b Reorder the terms: -35 + 2b + b2 = 3b Solving -35 + 2b + b2 = 3b Solving for variable 'b'. Reorder the terms: -35 + 2b + -3b + b2 = 3b + -3b Combine like terms: 2b + -3b = -1b -35 + -1b + b2 = 3b + -3b Combine like terms: 3b + -3b = 0 -35 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -1b + 35 + b2 = 0 + 35 Reorder the terms: -35 + 35 + -1b + b2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -1b + b2 = 0 + 35 -1b + b2 = 0 + 35 Combine like terms: 0 + 35 = 35 -1b + b2 = 35 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 35 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 35 + 0.25 Combine like terms: 35 + 0.25 = 35.25 0.25 + -1b + b2 = 35.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (b + -0.5) equal to 5.937171044 and -5.937171044.Subproblem 1
b + -0.5 = 5.937171044 Simplifying b + -0.5 = 5.937171044 Reorder the terms: -0.5 + b = 5.937171044 Solving -0.5 + b = 5.937171044 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 5.937171044 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 5.937171044 + 0.5 b = 5.937171044 + 0.5 Combine like terms: 5.937171044 + 0.5 = 6.437171044 b = 6.437171044 Simplifying b = 6.437171044Subproblem 2
b + -0.5 = -5.937171044 Simplifying b + -0.5 = -5.937171044 Reorder the terms: -0.5 + b = -5.937171044 Solving -0.5 + b = -5.937171044 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -5.937171044 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -5.937171044 + 0.5 b = -5.937171044 + 0.5 Combine like terms: -5.937171044 + 0.5 = -5.437171044 b = -5.437171044 Simplifying b = -5.437171044Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.437171044, -5.437171044}
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