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Simplifying b2 + -2b + -54 = 7 Reorder the terms: -54 + -2b + b2 = 7 Solving -54 + -2b + b2 = 7 Solving for variable 'b'. Reorder the terms: -54 + -7 + -2b + b2 = 7 + -7 Combine like terms: -54 + -7 = -61 -61 + -2b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 -61 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + -2b + 61 + b2 = 0 + 61 Reorder the terms: -61 + 61 + -2b + b2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -2b + b2 = 0 + 61 -2b + b2 = 0 + 61 Combine like terms: 0 + 61 = 61 -2b + b2 = 61 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 61 + 1 Reorder the terms: 1 + -2b + b2 = 61 + 1 Combine like terms: 61 + 1 = 62 1 + -2b + b2 = 62 Factor a perfect square on the left side: (b + -1)(b + -1) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (b + -1) equal to 7.874007874 and -7.874007874.Subproblem 1
b + -1 = 7.874007874 Simplifying b + -1 = 7.874007874 Reorder the terms: -1 + b = 7.874007874 Solving -1 + b = 7.874007874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 7.874007874 + 1 Combine like terms: -1 + 1 = 0 0 + b = 7.874007874 + 1 b = 7.874007874 + 1 Combine like terms: 7.874007874 + 1 = 8.874007874 b = 8.874007874 Simplifying b = 8.874007874Subproblem 2
b + -1 = -7.874007874 Simplifying b + -1 = -7.874007874 Reorder the terms: -1 + b = -7.874007874 Solving -1 + b = -7.874007874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -7.874007874 + 1 Combine like terms: -1 + 1 = 0 0 + b = -7.874007874 + 1 b = -7.874007874 + 1 Combine like terms: -7.874007874 + 1 = -6.874007874 b = -6.874007874 Simplifying b = -6.874007874Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.874007874, -6.874007874}
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