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Simplifying b2 + -20b + -3 = 0 Reorder the terms: -3 + -20b + b2 = 0 Solving -3 + -20b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -20b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + -20b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -20b + b2 = 0 + 3 -20b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 -20b + b2 = 3 The b term is -20b. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20b + 100 + b2 = 3 + 100 Reorder the terms: 100 + -20b + b2 = 3 + 100 Combine like terms: 3 + 100 = 103 100 + -20b + b2 = 103 Factor a perfect square on the left side: (b + -10)(b + -10) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (b + -10) equal to 10.148891565 and -10.148891565.Subproblem 1
b + -10 = 10.148891565 Simplifying b + -10 = 10.148891565 Reorder the terms: -10 + b = 10.148891565 Solving -10 + b = 10.148891565 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = 10.148891565 + 10 Combine like terms: -10 + 10 = 0 0 + b = 10.148891565 + 10 b = 10.148891565 + 10 Combine like terms: 10.148891565 + 10 = 20.148891565 b = 20.148891565 Simplifying b = 20.148891565Subproblem 2
b + -10 = -10.148891565 Simplifying b + -10 = -10.148891565 Reorder the terms: -10 + b = -10.148891565 Solving -10 + b = -10.148891565 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + b = -10.148891565 + 10 Combine like terms: -10 + 10 = 0 0 + b = -10.148891565 + 10 b = -10.148891565 + 10 Combine like terms: -10.148891565 + 10 = -0.148891565 b = -0.148891565 Simplifying b = -0.148891565Solution
The solution to the problem is based on the solutions from the subproblems. b = {20.148891565, -0.148891565}
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