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Simplifying b2 + -24b + -23 = 0 Reorder the terms: -23 + -24b + b2 = 0 Solving -23 + -24b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -24b + 23 + b2 = 0 + 23 Reorder the terms: -23 + 23 + -24b + b2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -24b + b2 = 0 + 23 -24b + b2 = 0 + 23 Combine like terms: 0 + 23 = 23 -24b + b2 = 23 The b term is -24b. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24b + 144 + b2 = 23 + 144 Reorder the terms: 144 + -24b + b2 = 23 + 144 Combine like terms: 23 + 144 = 167 144 + -24b + b2 = 167 Factor a perfect square on the left side: (b + -12)(b + -12) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (b + -12) equal to 12.922847983 and -12.922847983.Subproblem 1
b + -12 = 12.922847983 Simplifying b + -12 = 12.922847983 Reorder the terms: -12 + b = 12.922847983 Solving -12 + b = 12.922847983 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + b = 12.922847983 + 12 Combine like terms: -12 + 12 = 0 0 + b = 12.922847983 + 12 b = 12.922847983 + 12 Combine like terms: 12.922847983 + 12 = 24.922847983 b = 24.922847983 Simplifying b = 24.922847983Subproblem 2
b + -12 = -12.922847983 Simplifying b + -12 = -12.922847983 Reorder the terms: -12 + b = -12.922847983 Solving -12 + b = -12.922847983 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + b = -12.922847983 + 12 Combine like terms: -12 + 12 = 0 0 + b = -12.922847983 + 12 b = -12.922847983 + 12 Combine like terms: -12.922847983 + 12 = -0.922847983 b = -0.922847983 Simplifying b = -0.922847983Solution
The solution to the problem is based on the solutions from the subproblems. b = {24.922847983, -0.922847983}
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