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Simplifying b2 + -18b + 50 = -10 Reorder the terms: 50 + -18b + b2 = -10 Solving 50 + -18b + b2 = -10 Solving for variable 'b'. Reorder the terms: 50 + 10 + -18b + b2 = -10 + 10 Combine like terms: 50 + 10 = 60 60 + -18b + b2 = -10 + 10 Combine like terms: -10 + 10 = 0 60 + -18b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -18b + -60 + b2 = 0 + -60 Reorder the terms: 60 + -60 + -18b + b2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -18b + b2 = 0 + -60 -18b + b2 = 0 + -60 Combine like terms: 0 + -60 = -60 -18b + b2 = -60 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 = -60 + 81 Reorder the terms: 81 + -18b + b2 = -60 + 81 Combine like terms: -60 + 81 = 21 81 + -18b + b2 = 21 Factor a perfect square on the left side: (b + -9)(b + -9) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (b + -9) equal to 4.582575695 and -4.582575695.Subproblem 1
b + -9 = 4.582575695 Simplifying b + -9 = 4.582575695 Reorder the terms: -9 + b = 4.582575695 Solving -9 + b = 4.582575695 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 = 4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + b = 4.582575695 + 9 b = 4.582575695 + 9 Combine like terms: 4.582575695 + 9 = 13.582575695 b = 13.582575695 Simplifying b = 13.582575695Subproblem 2
b + -9 = -4.582575695 Simplifying b + -9 = -4.582575695 Reorder the terms: -9 + b = -4.582575695 Solving -9 + b = -4.582575695 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 = -4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + b = -4.582575695 + 9 b = -4.582575695 + 9 Combine like terms: -4.582575695 + 9 = 4.417424305 b = 4.417424305 Simplifying b = 4.417424305Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.582575695, 4.417424305}
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