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Simplifying b(b + -5) = 13 Reorder the terms: b(-5 + b) = 13 (-5 * b + b * b) = 13 (-5b + b2) = 13 Solving -5b + b2 = 13 Solving for variable 'b'. Reorder the terms: -13 + -5b + b2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -5b + 13 + b2 = 0 + 13 Reorder the terms: -13 + 13 + -5b + b2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -5b + b2 = 0 + 13 -5b + b2 = 0 + 13 Combine like terms: 0 + 13 = 13 -5b + b2 = 13 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 = 13 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 13 + 6.25 Combine like terms: 13 + 6.25 = 19.25 6.25 + -5b + b2 = 19.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (b + -2.5) equal to 4.387482194 and -4.387482194.Subproblem 1
b + -2.5 = 4.387482194 Simplifying b + -2.5 = 4.387482194 Reorder the terms: -2.5 + b = 4.387482194 Solving -2.5 + b = 4.387482194 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 = 4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 4.387482194 + 2.5 b = 4.387482194 + 2.5 Combine like terms: 4.387482194 + 2.5 = 6.887482194 b = 6.887482194 Simplifying b = 6.887482194Subproblem 2
b + -2.5 = -4.387482194 Simplifying b + -2.5 = -4.387482194 Reorder the terms: -2.5 + b = -4.387482194 Solving -2.5 + b = -4.387482194 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 = -4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -4.387482194 + 2.5 b = -4.387482194 + 2.5 Combine like terms: -4.387482194 + 2.5 = -1.887482194 b = -1.887482194 Simplifying b = -1.887482194Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.887482194, -1.887482194}
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