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Simplifying b2 + -42b + -41 = 0 Reorder the terms: -41 + -42b + b2 = 0 Solving -41 + -42b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -42b + 41 + b2 = 0 + 41 Reorder the terms: -41 + 41 + -42b + b2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -42b + b2 = 0 + 41 -42b + b2 = 0 + 41 Combine like terms: 0 + 41 = 41 -42b + b2 = 41 The b term is -42b. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42b + 441 + b2 = 41 + 441 Reorder the terms: 441 + -42b + b2 = 41 + 441 Combine like terms: 41 + 441 = 482 441 + -42b + b2 = 482 Factor a perfect square on the left side: (b + -21)(b + -21) = 482 Calculate the square root of the right side: 21.9544984 Break this problem into two subproblems by setting (b + -21) equal to 21.9544984 and -21.9544984.Subproblem 1
b + -21 = 21.9544984 Simplifying b + -21 = 21.9544984 Reorder the terms: -21 + b = 21.9544984 Solving -21 + b = 21.9544984 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + b = 21.9544984 + 21 Combine like terms: -21 + 21 = 0 0 + b = 21.9544984 + 21 b = 21.9544984 + 21 Combine like terms: 21.9544984 + 21 = 42.9544984 b = 42.9544984 Simplifying b = 42.9544984Subproblem 2
b + -21 = -21.9544984 Simplifying b + -21 = -21.9544984 Reorder the terms: -21 + b = -21.9544984 Solving -21 + b = -21.9544984 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + b = -21.9544984 + 21 Combine like terms: -21 + 21 = 0 0 + b = -21.9544984 + 21 b = -21.9544984 + 21 Combine like terms: -21.9544984 + 21 = -0.9544984 b = -0.9544984 Simplifying b = -0.9544984Solution
The solution to the problem is based on the solutions from the subproblems. b = {42.9544984, -0.9544984}
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