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Simplifying b2 + -4b + -53 = -4 Reorder the terms: -53 + -4b + b2 = -4 Solving -53 + -4b + b2 = -4 Solving for variable 'b'. Reorder the terms: -53 + 4 + -4b + b2 = -4 + 4 Combine like terms: -53 + 4 = -49 -49 + -4b + b2 = -4 + 4 Combine like terms: -4 + 4 = 0 -49 + -4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -4b + 49 + b2 = 0 + 49 Reorder the terms: -49 + 49 + -4b + b2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -4b + b2 = 0 + 49 -4b + b2 = 0 + 49 Combine like terms: 0 + 49 = 49 -4b + b2 = 49 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 = 49 + 4 Reorder the terms: 4 + -4b + b2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + -4b + b2 = 53 Factor a perfect square on the left side: (b + -2)(b + -2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (b + -2) equal to 7.280109889 and -7.280109889.Subproblem 1
b + -2 = 7.280109889 Simplifying b + -2 = 7.280109889 Reorder the terms: -2 + b = 7.280109889 Solving -2 + b = 7.280109889 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 = 7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + b = 7.280109889 + 2 b = 7.280109889 + 2 Combine like terms: 7.280109889 + 2 = 9.280109889 b = 9.280109889 Simplifying b = 9.280109889Subproblem 2
b + -2 = -7.280109889 Simplifying b + -2 = -7.280109889 Reorder the terms: -2 + b = -7.280109889 Solving -2 + b = -7.280109889 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 = -7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + b = -7.280109889 + 2 b = -7.280109889 + 2 Combine like terms: -7.280109889 + 2 = -5.280109889 b = -5.280109889 Simplifying b = -5.280109889Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.280109889, -5.280109889}
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