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Simplifying b2 + 18b + -72 = 0 Reorder the terms: -72 + 18b + b2 = 0 Solving -72 + 18b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 18b + 72 + b2 = 0 + 72 Reorder the terms: -72 + 72 + 18b + b2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 18b + b2 = 0 + 72 18b + b2 = 0 + 72 Combine like terms: 0 + 72 = 72 18b + b2 = 72 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 = 72 + 81 Reorder the terms: 81 + 18b + b2 = 72 + 81 Combine like terms: 72 + 81 = 153 81 + 18b + b2 = 153 Factor a perfect square on the left side: (b + 9)(b + 9) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (b + 9) equal to 12.369316877 and -12.369316877.Subproblem 1
b + 9 = 12.369316877 Simplifying b + 9 = 12.369316877 Reorder the terms: 9 + b = 12.369316877 Solving 9 + b = 12.369316877 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 = 12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + b = 12.369316877 + -9 b = 12.369316877 + -9 Combine like terms: 12.369316877 + -9 = 3.369316877 b = 3.369316877 Simplifying b = 3.369316877Subproblem 2
b + 9 = -12.369316877 Simplifying b + 9 = -12.369316877 Reorder the terms: 9 + b = -12.369316877 Solving 9 + b = -12.369316877 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 = -12.369316877 + -9 Combine like terms: 9 + -9 = 0 0 + b = -12.369316877 + -9 b = -12.369316877 + -9 Combine like terms: -12.369316877 + -9 = -21.369316877 b = -21.369316877 Simplifying b = -21.369316877Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.369316877, -21.369316877}
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