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Simplifying b2 + -4b + -14 = -1 Reorder the terms: -14 + -4b + b2 = -1 Solving -14 + -4b + b2 = -1 Solving for variable 'b'. Reorder the terms: -14 + 1 + -4b + b2 = -1 + 1 Combine like terms: -14 + 1 = -13 -13 + -4b + b2 = -1 + 1 Combine like terms: -1 + 1 = 0 -13 + -4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4b + 13 + b2 = 0 + 13 Reorder the terms: -13 + 13 + -4b + b2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4b + b2 = 0 + 13 -4b + b2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4b + b2 = 13 The b term is -4b. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4b + 4 + b2 = 13 + 4 Reorder the terms: 4 + -4b + b2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4b + b2 = 17 Factor a perfect square on the left side: (b + -2)(b + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (b + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
b + -2 = 4.123105626 Simplifying b + -2 = 4.123105626 Reorder the terms: -2 + b = 4.123105626 Solving -2 + b = 4.123105626 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + b = 4.123105626 + 2 b = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 b = 6.123105626 Simplifying b = 6.123105626Subproblem 2
b + -2 = -4.123105626 Simplifying b + -2 = -4.123105626 Reorder the terms: -2 + b = -4.123105626 Solving -2 + b = -4.123105626 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + b = -4.123105626 + 2 b = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 b = -2.123105626 Simplifying b = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.123105626, -2.123105626}
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