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Simplifying b2 + 9b + -9 = 10b Reorder the terms: -9 + 9b + b2 = 10b Solving -9 + 9b + b2 = 10b Solving for variable 'b'. Reorder the terms: -9 + 9b + -10b + b2 = 10b + -10b Combine like terms: 9b + -10b = -1b -9 + -1b + b2 = 10b + -10b Combine like terms: 10b + -10b = 0 -9 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -1b + 9 + b2 = 0 + 9 Reorder the terms: -9 + 9 + -1b + b2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1b + b2 = 0 + 9 -1b + b2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1b + b2 = 9 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 9 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1b + b2 = 9.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (b + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
b + -0.5 = 3.041381265 Simplifying b + -0.5 = 3.041381265 Reorder the terms: -0.5 + b = 3.041381265 Solving -0.5 + b = 3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 3.041381265 + 0.5 b = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 b = 3.541381265 Simplifying b = 3.541381265Subproblem 2
b + -0.5 = -3.041381265 Simplifying b + -0.5 = -3.041381265 Reorder the terms: -0.5 + b = -3.041381265 Solving -0.5 + b = -3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -3.041381265 + 0.5 b = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 b = -2.541381265 Simplifying b = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.541381265, -2.541381265}
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