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Simplifying 35 * 35 + -35b + -1b * b = 0 Multiply 35 * 35 1225 + -35b + -1b * b = 0 Multiply b * b 1225 + -35b + -1b2 = 0 Solving 1225 + -35b + -1b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1225 + 35b + b2 = 0 Move the constant term to the right: Add '1225' to each side of the equation. -1225 + 35b + 1225 + b2 = 0 + 1225 Reorder the terms: -1225 + 1225 + 35b + b2 = 0 + 1225 Combine like terms: -1225 + 1225 = 0 0 + 35b + b2 = 0 + 1225 35b + b2 = 0 + 1225 Combine like terms: 0 + 1225 = 1225 35b + b2 = 1225 The b term is 35b. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35b + 306.25 + b2 = 1225 + 306.25 Reorder the terms: 306.25 + 35b + b2 = 1225 + 306.25 Combine like terms: 1225 + 306.25 = 1531.25 306.25 + 35b + b2 = 1531.25 Factor a perfect square on the left side: (b + 17.5)(b + 17.5) = 1531.25 Calculate the square root of the right side: 39.131189606 Break this problem into two subproblems by setting (b + 17.5) equal to 39.131189606 and -39.131189606.Subproblem 1
b + 17.5 = 39.131189606 Simplifying b + 17.5 = 39.131189606 Reorder the terms: 17.5 + b = 39.131189606 Solving 17.5 + b = 39.131189606 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + b = 39.131189606 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + b = 39.131189606 + -17.5 b = 39.131189606 + -17.5 Combine like terms: 39.131189606 + -17.5 = 21.631189606 b = 21.631189606 Simplifying b = 21.631189606Subproblem 2
b + 17.5 = -39.131189606 Simplifying b + 17.5 = -39.131189606 Reorder the terms: 17.5 + b = -39.131189606 Solving 17.5 + b = -39.131189606 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + b = -39.131189606 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + b = -39.131189606 + -17.5 b = -39.131189606 + -17.5 Combine like terms: -39.131189606 + -17.5 = -56.631189606 b = -56.631189606 Simplifying b = -56.631189606Solution
The solution to the problem is based on the solutions from the subproblems. b = {21.631189606, -56.631189606}
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