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Simplifying (26 + -1b) * b = 104 Reorder the terms for easier multiplication: b(26 + -1b) = 104 (26 * b + -1b * b) = 104 (26b + -1b2) = 104 Solving 26b + -1b2 = 104 Solving for variable 'b'. Reorder the terms: -104 + 26b + -1b2 = 104 + -104 Combine like terms: 104 + -104 = 0 -104 + 26b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 104 + -26b + b2 = 0 Move the constant term to the right: Add '-104' to each side of the equation. 104 + -26b + -104 + b2 = 0 + -104 Reorder the terms: 104 + -104 + -26b + b2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + -26b + b2 = 0 + -104 -26b + b2 = 0 + -104 Combine like terms: 0 + -104 = -104 -26b + b2 = -104 The b term is -26b. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26b + 169 + b2 = -104 + 169 Reorder the terms: 169 + -26b + b2 = -104 + 169 Combine like terms: -104 + 169 = 65 169 + -26b + b2 = 65 Factor a perfect square on the left side: (b + -13)(b + -13) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (b + -13) equal to 8.062257748 and -8.062257748.Subproblem 1
b + -13 = 8.062257748 Simplifying b + -13 = 8.062257748 Reorder the terms: -13 + b = 8.062257748 Solving -13 + b = 8.062257748 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + b = 8.062257748 + 13 Combine like terms: -13 + 13 = 0 0 + b = 8.062257748 + 13 b = 8.062257748 + 13 Combine like terms: 8.062257748 + 13 = 21.062257748 b = 21.062257748 Simplifying b = 21.062257748Subproblem 2
b + -13 = -8.062257748 Simplifying b + -13 = -8.062257748 Reorder the terms: -13 + b = -8.062257748 Solving -13 + b = -8.062257748 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + b = -8.062257748 + 13 Combine like terms: -13 + 13 = 0 0 + b = -8.062257748 + 13 b = -8.062257748 + 13 Combine like terms: -8.062257748 + 13 = 4.937742252 b = 4.937742252 Simplifying b = 4.937742252Solution
The solution to the problem is based on the solutions from the subproblems. b = {21.062257748, 4.937742252}
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