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Simplifying b2 + -7b + -36 = 0 Reorder the terms: -36 + -7b + b2 = 0 Solving -36 + -7b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -7b + 36 + b2 = 0 + 36 Reorder the terms: -36 + 36 + -7b + b2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -7b + b2 = 0 + 36 -7b + b2 = 0 + 36 Combine like terms: 0 + 36 = 36 -7b + b2 = 36 The b term is -7b. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7b + 12.25 + b2 = 36 + 12.25 Reorder the terms: 12.25 + -7b + b2 = 36 + 12.25 Combine like terms: 36 + 12.25 = 48.25 12.25 + -7b + b2 = 48.25 Factor a perfect square on the left side: (b + -3.5)(b + -3.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (b + -3.5) equal to 6.946221995 and -6.946221995.Subproblem 1
b + -3.5 = 6.946221995 Simplifying b + -3.5 = 6.946221995 Reorder the terms: -3.5 + b = 6.946221995 Solving -3.5 + b = 6.946221995 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = 6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = 6.946221995 + 3.5 b = 6.946221995 + 3.5 Combine like terms: 6.946221995 + 3.5 = 10.446221995 b = 10.446221995 Simplifying b = 10.446221995Subproblem 2
b + -3.5 = -6.946221995 Simplifying b + -3.5 = -6.946221995 Reorder the terms: -3.5 + b = -6.946221995 Solving -3.5 + b = -6.946221995 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = -6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = -6.946221995 + 3.5 b = -6.946221995 + 3.5 Combine like terms: -6.946221995 + 3.5 = -3.446221995 b = -3.446221995 Simplifying b = -3.446221995Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.446221995, -3.446221995}
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