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Simplifying 81 = b(b + 18) Reorder the terms: 81 = b(18 + b) 81 = (18 * b + b * b) 81 = (18b + b2) Solving 81 = 18b + b2 Solving for variable 'b'. Reorder the terms: 81 + -18b + -1b2 = 18b + -18b + b2 + -1b2 Combine like terms: 18b + -18b = 0 81 + -18b + -1b2 = 0 + b2 + -1b2 81 + -18b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 81 + -18b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 18b + b2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 18b + 81 + b2 = 0 + 81 Reorder the terms: -81 + 81 + 18b + b2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 18b + b2 = 0 + 81 18b + b2 = 0 + 81 Combine like terms: 0 + 81 = 81 18b + b2 = 81 The b term is 18b. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18b + 81 + b2 = 81 + 81 Reorder the terms: 81 + 18b + b2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + 18b + b2 = 162 Factor a perfect square on the left side: (b + 9)(b + 9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (b + 9) equal to 12.727922061 and -12.727922061.Subproblem 1
b + 9 = 12.727922061 Simplifying b + 9 = 12.727922061 Reorder the terms: 9 + b = 12.727922061 Solving 9 + b = 12.727922061 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = 12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + b = 12.727922061 + -9 b = 12.727922061 + -9 Combine like terms: 12.727922061 + -9 = 3.727922061 b = 3.727922061 Simplifying b = 3.727922061Subproblem 2
b + 9 = -12.727922061 Simplifying b + 9 = -12.727922061 Reorder the terms: 9 + b = -12.727922061 Solving 9 + b = -12.727922061 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = -12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + b = -12.727922061 + -9 b = -12.727922061 + -9 Combine like terms: -12.727922061 + -9 = -21.727922061 b = -21.727922061 Simplifying b = -21.727922061Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.727922061, -21.727922061}
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