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Simplifying b2 + -5b + -35 = 3b Reorder the terms: -35 + -5b + b2 = 3b Solving -35 + -5b + b2 = 3b Solving for variable 'b'. Reorder the terms: -35 + -5b + -3b + b2 = 3b + -3b Combine like terms: -5b + -3b = -8b -35 + -8b + b2 = 3b + -3b Combine like terms: 3b + -3b = 0 -35 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -8b + 35 + b2 = 0 + 35 Reorder the terms: -35 + 35 + -8b + b2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -8b + b2 = 0 + 35 -8b + b2 = 0 + 35 Combine like terms: 0 + 35 = 35 -8b + b2 = 35 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = 35 + 16 Reorder the terms: 16 + -8b + b2 = 35 + 16 Combine like terms: 35 + 16 = 51 16 + -8b + b2 = 51 Factor a perfect square on the left side: (b + -4)(b + -4) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (b + -4) equal to 7.141428429 and -7.141428429.Subproblem 1
b + -4 = 7.141428429 Simplifying b + -4 = 7.141428429 Reorder the terms: -4 + b = 7.141428429 Solving -4 + b = 7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + b = 7.141428429 + 4 b = 7.141428429 + 4 Combine like terms: 7.141428429 + 4 = 11.141428429 b = 11.141428429 Simplifying b = 11.141428429Subproblem 2
b + -4 = -7.141428429 Simplifying b + -4 = -7.141428429 Reorder the terms: -4 + b = -7.141428429 Solving -4 + b = -7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + b = -7.141428429 + 4 b = -7.141428429 + 4 Combine like terms: -7.141428429 + 4 = -3.141428429 b = -3.141428429 Simplifying b = -3.141428429Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.141428429, -3.141428429}
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