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Simplifying b2 + -2b + -58 = -8 Reorder the terms: -58 + -2b + b2 = -8 Solving -58 + -2b + b2 = -8 Solving for variable 'b'. Reorder the terms: -58 + 8 + -2b + b2 = -8 + 8 Combine like terms: -58 + 8 = -50 -50 + -2b + b2 = -8 + 8 Combine like terms: -8 + 8 = 0 -50 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -2b + 50 + b2 = 0 + 50 Reorder the terms: -50 + 50 + -2b + b2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -2b + b2 = 0 + 50 -2b + b2 = 0 + 50 Combine like terms: 0 + 50 = 50 -2b + b2 = 50 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 = 50 + 1 Reorder the terms: 1 + -2b + b2 = 50 + 1 Combine like terms: 50 + 1 = 51 1 + -2b + b2 = 51 Factor a perfect square on the left side: (b + -1)(b + -1) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (b + -1) equal to 7.141428429 and -7.141428429.Subproblem 1
b + -1 = 7.141428429 Simplifying b + -1 = 7.141428429 Reorder the terms: -1 + b = 7.141428429 Solving -1 + b = 7.141428429 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 = 7.141428429 + 1 Combine like terms: -1 + 1 = 0 0 + b = 7.141428429 + 1 b = 7.141428429 + 1 Combine like terms: 7.141428429 + 1 = 8.141428429 b = 8.141428429 Simplifying b = 8.141428429Subproblem 2
b + -1 = -7.141428429 Simplifying b + -1 = -7.141428429 Reorder the terms: -1 + b = -7.141428429 Solving -1 + b = -7.141428429 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 = -7.141428429 + 1 Combine like terms: -1 + 1 = 0 0 + b = -7.141428429 + 1 b = -7.141428429 + 1 Combine like terms: -7.141428429 + 1 = -6.141428429 b = -6.141428429 Simplifying b = -6.141428429Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.141428429, -6.141428429}
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