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Simplifying b2 + -5b + -46 = 0 Reorder the terms: -46 + -5b + b2 = 0 Solving -46 + -5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -5b + 46 + b2 = 0 + 46 Reorder the terms: -46 + 46 + -5b + b2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -5b + b2 = 0 + 46 -5b + b2 = 0 + 46 Combine like terms: 0 + 46 = 46 -5b + b2 = 46 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 = 46 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 46 + 6.25 Combine like terms: 46 + 6.25 = 52.25 6.25 + -5b + b2 = 52.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (b + -2.5) equal to 7.228416147 and -7.228416147.Subproblem 1
b + -2.5 = 7.228416147 Simplifying b + -2.5 = 7.228416147 Reorder the terms: -2.5 + b = 7.228416147 Solving -2.5 + b = 7.228416147 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 = 7.228416147 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 7.228416147 + 2.5 b = 7.228416147 + 2.5 Combine like terms: 7.228416147 + 2.5 = 9.728416147 b = 9.728416147 Simplifying b = 9.728416147Subproblem 2
b + -2.5 = -7.228416147 Simplifying b + -2.5 = -7.228416147 Reorder the terms: -2.5 + b = -7.228416147 Solving -2.5 + b = -7.228416147 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 = -7.228416147 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -7.228416147 + 2.5 b = -7.228416147 + 2.5 Combine like terms: -7.228416147 + 2.5 = -4.728416147 b = -4.728416147 Simplifying b = -4.728416147Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.728416147, -4.728416147}
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